Free Ideal Rings and Localization in General Rings

Preface Note to the reader Terminology, notations and conventions used List of special notation 0. Preliminaries on modules 1. Principal ideal domains 2. Firs, semifirs and the weak algorithm 3. Factorization 4. 2-firs with a distributive factor lattice 5. Modules over firs and semifirs 6. Centralizers and subalgebras 7. Skew fields of fractions Appendix Bibliography and author index Subject index.

[1]  W. Leavitt ADDITIVE CATEGORIES AND A THEOREM OF , 2007 .

[2]  Joseph L. Taylor,et al.  BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 79 , Number 1 , January 1973 FUNCTIONS OF SEVERAL NONCOMMUTING VARIABLES , 2007 .

[3]  P. Menal A REMARK ON POWER SERIES RINGS , 2006 .

[4]  Julia Collins,et al.  HOMOLOGICAL ALGEBRA , 2021, Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34.

[5]  Christian Ausoni,et al.  AN INTRODUCTION TO ALGEBRAIC K-THEORY , 2005 .

[6]  Vitor O. Ferreira,et al.  A Hopf-Galois correspondence for free algebras , 2004 .

[7]  V. Shpilrain,et al.  Combinatorial Methods: Free Groups, Polynomials, and Free Algebras , 2003 .

[8]  F. Cedó,et al.  Inverting Elements in Rigid Monoids , 2003 .

[9]  G. Bergman Constructing division rings as module-theoretic direct limits , 2002 .

[10]  Vitor O. Ferreira Constants of derivations on free associative algebras , 2002, Glasgow Mathematical Journal.

[11]  P. Cohn Localization in general rings a historical survey , 2002 .

[12]  P. Cohn THE AUTOMORPHISM GROUP OF THE FREE ALGEBRA OF RANK TWO , 2002 .

[13]  Desmond Sheiham Non‐Commutative Characteristic Polynomials and Cohn Localization , 2001, math/0104158.

[14]  L. Gerritzen,et al.  On the Group of Symplectic Matrices Over a Free Associative Algebra , 2001 .

[15]  Vitor O. Ferreira COMMUTATIVE MONOID AMALGAMS WITH NATURAL CORE , 2001 .

[16]  P. Cohn On the Construction of Sylvester Domains , 2000 .

[17]  Vitor O. Ferreira Tensor Rings under Field Extensions , 2000 .

[18]  N. Iyudu Subalgebra membership problem and subalgebra standard basis , 2000 .

[19]  N. Kim,et al.  On von neumann regular rings , 2000 .

[20]  P. Cohn From Hermite rings to Sylvester domains , 1999 .

[21]  P. M. COHN,et al.  On the Construction of the Free Field , 1999, Int. J. Algebra Comput..

[22]  D. I. Piontkovskii On free products in varieties of associative algebras , 1999 .

[23]  P. Cohn,et al.  The skew field of rational functions on the quantum plane , 1999 .

[24]  A. Tuganbaev Semidistributive modules , 1999 .

[25]  G. Bergman Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups , 1999 .

[26]  C. Reutenauer Malcev-Neumann series and the free fleld , 1999 .

[27]  L. Gerritzen On infinite Gröbner bases in free algebras , 1998 .

[28]  Alexander A. Mikhalev,et al.  Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I Free Associative Algebras , 1998, Int. J. Algebra Comput..

[29]  M. Shirvani,et al.  Free Group Algebras in the Field of Fractions of Differential Polynomial Rings and Enveloping Algebras , 1998 .

[30]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[31]  R. Antoine On rigid monoids with right ACC1 , 1998 .

[32]  Askar A. Tuganbaev,et al.  Rings of quotients , 1998 .

[33]  P. Cohn Cyclic Artinian Modules without a Composition Series , 1997 .

[34]  F. Cedó Strongly prime power series rings , 1997 .

[35]  P. M. Cohn,et al.  The universal skew field of fractions ofa tensor product of free rings , 1997 .

[36]  M. Shirvani,et al.  Free Group Algebras in Certain Division Rings , 1996 .

[37]  Christophe Reutenauer,et al.  Inversion height in free fields , 1996 .

[38]  Katsuo Chiba Free Subgroups and Free Subsemigroups of Division Rings , 1996 .

[39]  V. Govorov On Poincaré series for codes , 1996 .

[40]  U. Umirbaev Universal derivations and subalgebras of free algebras , 1996 .

[41]  S. Vovsi,et al.  On fully invariant ideals of the free group algebra , 1996 .

[42]  M. Shirvani,et al.  On free group algebras in division rings with uncountable center , 1996 .

[43]  M. J. Evans SOME RINGS WITH MANY NON-FREE STABLY FREE MODULES , 1995 .

[44]  S. Farbman NON-FREE TWO-GENERATOR SUBGROUPS OF SL2(Q) , 1995 .

[45]  F. Cedó,et al.  The ore condition for polynomial and power series rings , 1995 .

[46]  Tong Wenting IBN rings and orderings on grothendieck groups , 1994 .

[47]  Sergey Pinchuk,et al.  A counterexamle to the strong real Jacobian conjecture , 1994 .

[48]  C. Reutenauer,et al.  A Normal Form in Free Fields , 1994, Canadian Journal of Mathematics.

[49]  F. Cedó,et al.  Construction of Left Fir Monoid Rings , 1994 .

[50]  T. Palmer Banach algebras and the general theory of *-algebras , 1994 .

[51]  A. Rosenmann,et al.  IDEALS OF FINITE CODIMENSION IN FREE ALGEBRAS AND THE FC-LOCALIZATION , 1994 .

[52]  Amnon Rosenmann,et al.  Essentiality of Fractal ideals , 1993, Int. J. Algebra Comput..

[53]  P. Malcolmson Weakly Finite Matrix Localizations , 1993 .

[54]  S. Vovsi On the semigroups of fully invariant ideals of the free group algebra and the free associative algebra , 1993 .

[55]  Guy Melançon,et al.  Constructions des bases standard des K-modules à droite , 1993, Theor. Comput. Sci..

[56]  M. Farber,et al.  The Cohn localization of the free group ring , 1992, Mathematical Proceedings of the Cambridge Philosophical Society.

[57]  A. A. Klein Free subsemigroups of domains , 1992 .

[58]  J. Lorimer The classification of compact right chain rings , 1992 .

[59]  F. Cedó,et al.  On rigid monoids and 2-fir monoid rings , 1992 .

[60]  M. Mike Universal localization and triangular rings , 1992 .

[61]  G. Cauchon,et al.  Séries de Malcev-Neumann sur le groupe libre et questions de ratonalité , 1992, Theor. Comput. Sci..

[62]  S. Westreich On Sylvester Rank Functions , 1991 .

[63]  L. Makar-Limanov,et al.  Free subalgebras of enveloping fields , 1991 .

[64]  Daniel Krob,et al.  Some Examples of Formal Series Used in Non-Commutative Algebra , 1991, Theoretical Computer Science.

[65]  H. Marubayashi,et al.  Non commutative unique factorization rings , 1991 .

[66]  V. Kharchenko The Galois Theory of Prime Rings , 1991 .

[67]  George M. Bergman,et al.  Ordering coproducts of groups and semigroups , 1990 .

[68]  Ernst Specker,et al.  Additive Gruppen von Folgen Ganzer Zahlen , 1990 .

[69]  N. Jacobson,et al.  Basic Algebra II , 1989 .

[70]  A. Tuganbaev Modules whose lattice of submodules is distributive , 1989 .

[71]  F. Bonang Noetherian rings whose subidealizer subrings have pan-a.c.c , 1989 .

[72]  F. Cedó On semifir monoid rings , 1989 .

[73]  P. Cohn Distributive factor lattices in free rings , 1989 .

[74]  Jean Berstel,et al.  Rational series and their languages , 1988, EATCS monographs on theoretical computer science.

[75]  R. Beauregard Left Ore principal right ideal domains , 1988 .

[76]  F. Cedó A question of cohn on semifir monoid rings , 1988 .

[77]  A. Schofield,et al.  On semihereditary rings , 1988 .

[78]  J. Lewin The symmetric ring of quotients of a 2-fir , 1988 .

[79]  André Leroy,et al.  Algebraic Conjugacy Classes and Skew Polynomial Rings , 1988 .

[80]  M. C. Hedges The Freiheitssatz for Graded Algebras , 1987 .

[81]  G. Bergman Normalizers of Semifirs in Their Universal Fields , 1987 .

[82]  D. Passman,et al.  Prime ideals in fixed rings of free algebras , 1987 .

[83]  M. Lorenz On free subalgebras of certain division algebras , 1986 .

[84]  H. Brungs Bezout Domains and Rings with a Distributive Lattice of Right Ideals , 1976, Canadian Journal of Mathematics.

[85]  M. Voskoglou Extending derivations and endomorphisms to skew polynomial rings. , 1986 .

[86]  Warren Dicks On the cohomology of one-relator associative algebras , 1985 .

[87]  A. Schofield Representations of Rings Over Skew Fields , 1985 .

[88]  Gert Almkvist,et al.  Hilbert series of fixed free algebras and noncommutative classical invariant theory , 1985 .

[89]  L. Makar-Limanov Algebraically closed skew fields , 1985 .

[90]  C. Ringel,et al.  A class of bounded hereditary noetherian domains , 1985 .

[91]  Warren Dicks Homogeneous elements of free algebras have free idealizers , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[92]  J. T. Stafford Stably free, projective right ideals , 1985 .

[93]  P. Cohn,et al.  Two Examples of Principal Ideal Domains , 1985 .

[94]  P. Cohn The Universal Field of Fractions of a Semifir: III. Centralizers and Normalizers , 1985 .

[95]  A. Leroy Derivees logarithmiques pour une s-derivation algebrique , 1985 .

[96]  P. Cohn The Universal Field of Fractions of a Semifir II. The Depth , 1985 .

[97]  G. Revesz,et al.  On a construction of the universal field of fractions of a free algebra , 1984 .

[98]  M. Roberts Endomorphism Rings of Finitely Presented Modules over Free Algebras , 1984 .

[99]  H. Mez HNN-extensions of algebras and applications , 1984, Bulletin of the Australian Mathematical Society.

[100]  G. Törner,et al.  Skew power series rings and derivations , 1984 .

[101]  V. Kharchenko Noncommutative invariants of finite groups and Noetherian varieties , 1984 .

[102]  J. Beachy On noncommutative localization , 1984 .

[103]  L. Makar-Limanov On free subsemigroups of skew fields , 1984 .

[104]  A. Chatters Non-commutative unique factorization domains , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[105]  H. Nakajima Regular rings of invariants of unipotent groups , 1983 .

[106]  M. Prest Existentially Complete Prime Rings , 1983 .

[107]  Warren Dicks A Free Algebra can Be Free as a Module over a Nonfree Subalgebra , 1983 .

[108]  G. Whaples,et al.  Polynomials with Coefficients from a Division Ring , 1983, Canadian Journal of Mathematics.

[109]  S. Montgomery,et al.  The normal closure of coproducts of domains , 1983 .

[110]  Warren Dicks The HNN construction for rings , 1983 .

[111]  G. Révész On the abelianized multiplicative group of a universal field of fractions , 1983 .

[112]  R. L. Snider The division ring of fractions of a group ring , 1983 .

[113]  S. Montgomery Von neuman finiteness of tensor products of algebras , 1983 .

[114]  G. Bergman Sfields finitely right-generated over subrings , 1983 .

[115]  L. Makar-Limanov The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra , 1983 .

[116]  Warren Dicks,et al.  Free algebras over Bezout domains are Sylvester domains , 1983 .

[117]  P. Helm Generators and relations for certain linear groups over rings of linear operators , 1983 .

[118]  Charles Ching-an Cheng,et al.  Hereditary Monoid Rings , 1982 .

[119]  H. Bass,et al.  The Jacobian conjecture: Reduction of degree and formal expansion of the inverse , 1982 .

[120]  Warren Dicks,et al.  Poincare series and a problem of S. Montgomery , 1982 .

[121]  W. S. Martindale The Extended Center of Coproducts , 1982, Canadian Mathematical Bulletin.

[122]  P. Cohn,et al.  On the law of nullity , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.

[123]  M. Hezavehi Matrix valuations and their associated skew fields , 1982 .

[124]  J. W. Kerr The power series ring over an Ore domain need not be Ore , 1982 .

[125]  P. Cohn The divisor group of a fir , 1982 .

[126]  Abraham Zaks Atomic rings without a.c.c. on principal ideals , 1982 .

[127]  P. Cohn The Universal Field of Fractions of a Semifir I. Numerators and Denominators , 1982 .

[128]  John Dauns,et al.  A concrete approach to division rings , 1982, Research and education in mathematics.

[129]  P. Cohn Torsion modules and the factorization of matrices , 1982 .

[130]  P. Malcolmson Construction of universal matrix localizations , 1982 .

[131]  P. Menal The monoid rings that are Bezout domains , 1981 .

[132]  G. Törner,et al.  Right chain rings and the generalized semigroup of divisibility. , 1981 .

[133]  Warren Dicks,et al.  An exact sequence for rings of polynomials in partly commuting indeterminates , 1981 .

[134]  M. Roberts Normal forms, factorizations and eigenrings in free algebras , 1981 .

[135]  A. A. Klein Some ring-theoretic properties implied by embeddability in fields , 1980 .

[136]  P. Malcolmson Determining homomorphisms to skew fields , 1980 .

[137]  R. Beauregard Left versus right LCM domains , 1980 .

[138]  P. Cohn,et al.  On central extensions of skew fields , 1980 .

[139]  P. Russell Hamburger-Noether expansions and approximate roots of polynomials , 1980 .

[140]  P. Cohn On Semifir Constructions , 1980 .

[141]  P. Cohn,et al.  Extensions of valuations on skew fields , 1980 .

[142]  A. Macintyre Combinatorial Problems for Skew Fields I. Analogue of Britton's Lemma, and Results of Adjan-Rabin Type , 1979 .

[143]  Warren Dicks Hereditary Group Rings , 1979 .

[144]  Richard P. Stanley,et al.  Invariants of finite groups and their applications to combinatorics , 1979 .

[145]  Warren Dicks,et al.  The Group Rings that are Semifirs , 1979 .

[146]  C. Ringel The spectrum of a finite dimensional algebra , 1979 .

[147]  G. Bergman,et al.  Universal derivations and universal ring constructions , 1978 .

[148]  P. Vámos Finitely Generated Artinian and Distributive Modules are Cyclic , 1978 .

[149]  Peter Malcolmson,et al.  A Prime Matrix Ideal Yields a Skew Field , 1978 .

[150]  Armin Leutbecher Euklidischer Algorithmus und die Gruppe GL2 , 1978 .

[151]  H. Brungs Unique factorization in rings with right ACC1 , 1978, Glasgow Mathematical Journal.

[152]  J. Lewin,et al.  An embedding of the group algebra of a torsion-free one-relator group in a field , 1978 .

[153]  T. W. D. Jooste Primitive derivations in free associative algebras , 1978 .

[154]  James Whitehead,et al.  PROJECTIVE MODULES , 2011 .

[155]  George M. Bergman,et al.  On the existence of subalgebras of direct products with prescribedd-fold projections , 1977 .

[156]  M. Roitman Completing unimodular rows to invertible matrices , 1977 .

[157]  K. Choo Grothendieck groups of twisted free associative algebras , 1977, Glasgow Mathematical Journal.

[158]  Warren Dicks Mayer‐Vietoris Presentations Over Colimits of Rings , 1977 .

[159]  S. Jøndrup The Centre of a Right Hereditary Ring , 1977 .

[160]  R. Beauregard,et al.  Left and right invariance in an integral domain , 1977 .

[161]  J. Lewin,et al.  Ranks of matrices over Ore domains , 1977 .

[162]  G. Bergman Rational relations and rational identities in division rings , 1976 .

[163]  T. Lam SERIES SUMMATION OF STABLY FREE MODULES , 1976 .

[164]  J. Hiblot Sur les anneaux euclidiens , 1976 .

[165]  P. Vámos Test modules and cogenerators , 1976 .

[166]  G. Bergman,et al.  The Semigroup of Ideals of a Fir is (Usually) Free , 1975 .

[167]  J. Goursaud,et al.  Anneaux de groupe héréditaires et semi-héréditaires , 1975 .

[168]  R. Tyler On the Lower Central Factors of a Free Associative Ring , 1975, Canadian Journal of Mathematics.

[169]  D. R. Lane Fixed Points of Affine Cremona Transformations of the Plane Over an Algebraically Closed Field , 1975 .

[170]  R. Sridharan,et al.  Protective modules over polynomial rings over division rings , 1975 .

[171]  B. Stenström Rings of Fractions , 1975 .

[172]  G. Bergman Modules over coproducts of rings , 1974 .

[173]  G. Bergman Coproducts and some universal ring constructions , 1974 .

[174]  H. Brungs Right Invariant Right Hereditary Rings , 1974, Canadian Journal of Mathematics.

[175]  P. Cohn The Class of Rings Embeddable in Skew Fields , 1974 .

[176]  Anne Grams,et al.  Atomic rings and the ascending chain condition for principal ideals , 1974, Mathematical Proceedings of the Cambridge Philosophical Society.

[177]  Jacques Lewin,et al.  Fields of fractions for group algebras of free groups , 1974 .

[178]  P. Cohn Localization in Semifirs , 1974 .

[179]  P. Cohn Progress in free associative algebras , 1974 .

[180]  J. L. Fisher The category of epic R-fields , 1974 .

[181]  K. Choo Whitehead Groups of twisted free associative algebras. , 1974 .

[182]  J. Lewin A matrix representation for associative algebras. II , 1974 .

[183]  J. L. Fisher The poset of skew fields generated by a free algebra , 1974 .

[184]  J. Lewin On some infinitely presented associative algebras , 1973, Journal of the Australian Mathematical Society.

[185]  S. Moran Some subalgebra theorems , 1973 .

[186]  P. Cohn The similarity reduction of matrices over a skew field , 1973 .

[187]  J. Silvester On the K2 of a Free Associative Algebra , 1973 .

[188]  G. Bergman Infinite multiplication of ideals in ℵ0-hereditary rings , 1973 .

[189]  J. Cozzens Simple principal left ideal domains , 1972 .

[190]  I. Beck Projective and free modules , 1972 .

[191]  Warren Dicks On One‐Relator Associative Algebras , 1972 .

[192]  J. Robson,et al.  Idealizers and hereditary noetherian prime rings , 1972 .

[193]  George M. Bergman,et al.  Boolean Rings of Projection Maps , 1972 .

[194]  J. Lewin A note on zero divisors in group-rings , 1972 .

[195]  A. A. Klein Involutorial division rings with arbitrary centers , 1972 .

[196]  G. Bergman HEREDITARILY AND COHEREDITARILY PROJECTIVE MODULES , 1972 .

[197]  P. Cohn Skew fields of fractions, and the prime spectrum of a general ring , 1972 .

[198]  Arun Vinayak Jategaonkar,et al.  Skew polynomial rings over semisimple rings , 1971 .

[199]  G. Bergman Hereditary Commutative Rings and Centres of Hereditary Rings , 1971 .

[200]  Paul M. Cohn,et al.  The Embedding of Firs in Skew Fields , 1971 .

[201]  A. Czerniakiewicz Automorphisms of a free associative algebra of rank 2. II , 1971 .

[202]  G. Bergman Groups Acting on Hereditary Rings , 1971 .

[203]  P. Cohn,et al.  The Centres of 2-Firs and Hereditary Rings , 1971 .

[204]  B. Osofsky On twisted polynomial rings , 1971 .

[205]  G. Baumslag,et al.  On Ascending Chain Conditions , 1971 .

[206]  Jean Carcanague Idéaux bilatères d'un anneau de polynomes non commutatifs sur un corps , 1971 .

[207]  J. L. Fisher Embedding free algebras in skew fields , 1971 .

[208]  P. Cohn,et al.  Bounded and invariant elements in 2-firs , 1971, Mathematical Proceedings of the Cambridge Philosophical Society.

[209]  T. W. D. Jooste Derivations in free power series rings and free associative algebras , 1971 .

[210]  H. Brungs Overrings of principal ideal domains , 1971 .

[211]  P. Cohn Torsion and protorsion modules over free ideal rings , 1970, Journal of the Australian Mathematical Society.

[212]  J. T. Knight On epimorphisms of non-commutative rings , 1970, Mathematical Proceedings of the Cambridge Philosophical Society.

[213]  Michel Fliess,et al.  Deux applications de la representation matricielle d'une serie rationnelle non commutative , 1970, SWAT.

[214]  John Dauns Integral domains that are not embeddable in division rings , 1970 .

[215]  I. Hughes Division Rings of Fractions for Group Rings , 1970 .

[216]  R. E. Johnson,et al.  PRIMARY FACTORIZATION IN A WEAK BEZOUT DOMAIN , 1970 .

[217]  P. Cohn On a class of rings with inverse weak algorithm , 1970 .

[218]  A. V. D. Water A property of torsion-free modules over left Ore domains , 1970 .

[219]  John Dauns Embeddings in division rings , 1970 .

[220]  J. Lewin Free modules over free algebras and free group algebras: The Schreier technique , 1969 .

[221]  R. E. Williams A note on rings with a weak algorithm , 1969 .

[222]  Melvin Hochster,et al.  Prime ideal structure in commutative rings , 1969 .

[223]  Arun Vinayak Jategaonkar,et al.  A counter-example in ring theory and homological algebra☆ , 1969 .

[224]  R. Beauregard,et al.  Infinite primes and unique factorization in a principal right ideal domain , 1969 .

[225]  C. U. Jensen Some cardinality questions for flat modules and coherence , 1969 .

[226]  A. V. Jategaonkar Rings with transfinite left division algorithm , 1969 .

[227]  A. A. Klein Necessary conditions for embedding rings into fields , 1969 .

[228]  M. Ikeda Über die maximalen Ideale einer freien assoziativen Algebra , 1969 .

[229]  R. E. Williams On the free product of rings with weak algorithm , 1969 .

[230]  G. Bergman Centralizers in free associative algebras , 1969 .

[231]  P. Cohn Free Associative Algebras , 1969 .

[232]  H. Brungs Generalized Discrete Valuation Rings , 1969, Canadian Journal of Mathematics.

[233]  P. Cohn Dependence in rings. II. The dependence number , 1969 .

[234]  George M. Bergman,et al.  Symmetric Elements in Free Powers of Rings , 1969 .

[235]  P. Cohn Factorization in general rings and strictly cyclic modules. , 1969 .

[236]  John Stallings,et al.  On Torsion-Free Groups with Infinitely Many Ends , 1968 .

[237]  M. Knus Homology and homomorphisms of rings , 1968 .

[238]  P. M. Cohn,et al.  Bezout rings and their subrings , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.

[239]  G. Nöbeling Verallgemeinerung eines Satzes von Herrn E. Specker , 1968 .

[240]  J. Lewin,et al.  On ideals of free associative algebras generated by a single element , 1968 .

[241]  J. Lewin ON SCHREIER VARIETIES OF LINEAR ALGEBRAS , 1968 .

[242]  I. G. MacDonald Algebraic geometry : introduction to schemes , 1968 .

[243]  J. Dixmier Sur les algèbres de Weyl , 1968 .

[244]  Maurice Nivat,et al.  Transduction des langages de Chomsky , 1968 .

[245]  R. M. Dicker A Set of Independent Axioms for a Field and a Condition for a Group to be the Multiplicative Group of a Field , 1968 .

[246]  J. Robson Rings in Which Finitely Generated Right Ideals are Principal , 1967 .

[247]  P. Cohn Torsion Modules Over Free Ideal Rings , 1967 .

[248]  A. A. Klein Rings nonembeddable in fields with multiplicative semigroups embeddable in groups , 1967 .

[249]  T. Smits Skew polynomial rings and nilpotent derivations , 1967 .

[250]  R. Hirsch A Note on Non-Commutative Polynomial Rings Subject to Degree-Preservation , 1967 .

[251]  J. Roos Locally distributive spectral categories and strongly regular rings. : 1967 Reports of the Midwest Category Seminar , 1967 .

[252]  S. A. Amitsur Rational identities and applications to algebra and geometry , 1966 .

[253]  P. Cohn Hereditary Local Rings , 1966, Nagoya Mathematical Journal.

[254]  P. Cohn A remark on matrix rings over free ideal rings , 1966, Mathematical Proceedings of the Cambridge Philosophical Society.

[255]  D. Dubois Modules of Sequences of Elements of a Ring , 1966 .

[256]  G. G. Gilbert THE MULTIPLICATIVE SEMIGROUP OF A RING , 1966 .

[257]  David Lissner Outer product rings , 1965 .

[258]  B. Gordon,et al.  On the zeros of polynomials over division rings , 1965 .

[259]  R. E. Johnson Unique factorization in a principal right ideal domain , 1965 .

[260]  S. A. Amitsur Generalized polynomial identities and pivotal monomials , 1965 .

[261]  W. Stephenson Characterizations of rings and modules by means of lattices. , 1965 .

[262]  S. Gersten Whitehead groups of free associative algebras , 1965 .

[263]  H. Bass Projective modules over free groups are free , 1964 .

[264]  P. Cohn Subalgebras of Free Associative Algebras , 1964 .

[265]  P. Cohn Free ideal rings , 1964 .

[266]  C. U. Jensen On Characterizations of Prüfer Rings. , 1963 .

[267]  Paul M. Cohn,et al.  Rings with a weak algorithm , 1963 .

[268]  P. M. Cohn,et al.  Factorization in Non-Commutative Power Series Rings , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[269]  P. M. Cohn,et al.  On subsemigroups of free semigroups , 1962 .

[270]  G. Higman,et al.  Embedding Theorems for Groups , 1949, Proceedings of the Edinburgh Mathematical Society.

[271]  E. Feller Factorization and lattice theorems for a bounded principal ideal domain , 1961 .

[272]  S. Chase A Generalization of the Ring of Triangular Matrices , 1961, Nagoya Mathematical Journal.

[273]  F. Albrecht On projective modules over semi-hereditary rings , 1961 .

[274]  Paul M. Cohn,et al.  On a Generalization of the Euclidean Algorithm , 1961, Mathematical Proceedings of the Cambridge Philosophical Society.

[275]  P. Cohn Quadratic Extensions of Skew Fields , 1961 .

[276]  Paul M. Cohn,et al.  On the Embedding of Rings in Skew Fields , 1961 .

[277]  E. Gentile On rings with one-sided field of quotients , 1960 .

[278]  E. Feller Intersection Irreducible Ideals of a Non-Commutative Principal Ideal Domain , 1960, Canadian Journal of Mathematics.

[279]  Paul M. Cohn,et al.  On the free product of associative rings , 1959 .

[280]  H. Nagao On GL(2, K[x]) , 1959 .

[281]  A. Goldie The Structure of Prime Rings Under Ascending Chain Conditions , 1958 .

[282]  J. McLeod ON THE COMMUTATOR SUBRING , 1958 .

[283]  M. Nagata A remark on the unique factorization theorem , 1957 .

[284]  Brockway McMillan,et al.  Two inequalities implied by unique decipherability , 1956, IRE Trans. Inf. Theory.

[285]  H. Claus Über die Partialbruchzerlegung in nicht notwendig kommutativen euklidischen Ringen. , 1955 .

[286]  R. Fox,et al.  Free differential calculus. I : Derivation in the free group ring , 1953 .

[287]  Shin-ichi Matsushita Topological Groups , 1952 .

[288]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[289]  J. Shepherdson Inverses and Zero Divisors in Matrix Rings , 1951 .

[290]  Nathan Jacobson,et al.  Some Remarks on One-Sided Inverses , 1950 .

[291]  Hans-Heinrich Ostmann Euklidische Ringe mit eindeutiger Partialbruchzerlegung. , 1950 .

[292]  Irving Kaplansky,et al.  Elementary divisors and modules , 1949 .

[293]  Leon Gordon Kraft,et al.  A device for quantizing, grouping, and coding amplitude-modulated pulses , 1949 .

[294]  B. H. Neumann,et al.  On ordered division rings , 1949 .

[295]  J. Dieudonné,et al.  Les déterminants sur un corps non commutatif , 1943 .

[296]  Heinrich W. E. Jung Über ganze birationale Transformationen der Ebene. , 1942 .

[297]  W. Magnus Über Gruppen und zugeordneten Liesche Ringe. , 1940 .

[298]  G. Higman,et al.  The Units of Group‐Rings , 1940 .

[299]  H. Serbin Factorization in principal ideal rings , 1938 .

[300]  T. Nakayama A note on the elementary divisor theory in non-commutative domains , 1938 .

[301]  A. Malcev On the immersion of an algebraic ring into a field , 1937 .

[302]  K. Hirsch A Note on Non-Commutative Polynomials , 1937 .

[303]  H. Fitting Primärkomponentenzerlegung in nichtkommutativen Ringen , 1935 .

[304]  O. Ore Theory of Non-Commutative Polynomials , 1933 .

[305]  O. Ore On a special class of polynomials , 1933 .

[306]  Oystein Ore,et al.  Linear Equations in Non-Commutative Fields , 1931 .

[307]  K. Hensel Über Systeme in einfachen Körpern. , 1929 .

[308]  W. Krull Zur Theorie der zweiseitigen Ideale in nichtkommutativen Bereichen , 1928 .

[309]  H. Hasse Über eindeutige Zerlegung in Primelemente oder in Primhauptideale in Integritätsbereichen. , 1928 .

[310]  K. Hensel Über eindeutige Zerlegung in Primelemente. , 1927 .

[311]  J. Wedderburn On division algebras , 1921 .

[312]  D. Hilbert,et al.  Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen , 2009 .

[313]  R. Dedekind,et al.  Ueber die von drei Moduln erzeugte Dualgruppe , 1900 .

[314]  E. Lady Unique Factorization , 2022 .