Hyman Bass and Ubiquity: Gorenstein Rings

This paper is based on a talk given by the author in October, 1997 at a conference at Columbia University in celebration of Hyman Bass's 65th birthday. The paper details some of the history of Gorenstein rings and their uses.

[1]  Christian Peskine,et al.  Dimension projective finie et cohomologie locale , 1973 .

[2]  L. L. Avramov,et al.  Locally Gorenstein homomorphisms , 1992 .

[3]  A. Grothendieck.  Théorèmes de dualité pour les faisceaux algébriques cohérents , 1958 .

[4]  F. S. Macaulay.  On the resolution of a given modular system into primary systems including some properties of Hilbert numbers , 1913 .

[5]  M. Bridger,et al.  Stable Module Theory , 1969 .

[6]  W. Gröbner,et al.  Über irreduzible Ideale in kommutativen Ringen , 1935 .

[7]  B. Ulrich,et al.  Divisor Class Groups and Deformations , 1985 .

[8]  J. Weier.  Un théorème d'intersection , 1957 .

[9]  D. Eisenbud.  Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[10]  R. Stanley.  Hilbert functions of graded algebras , 1978 .

[11]  M. Hochster.  Topics in the Homological Theory of Modules over Commutative Rings , 1975 .

[12]  A. Kustin,et al.  Structure theory for a class of grade four Gorenstein ideals , 1982 .

[13]  A. Iarrobino.  Associated Graded Algebra of a Gorenstein Artin Algebra , 1994 .

[14]  M. Hochster.  Cyclic purity versus purity in excellent Noetherian rings , 1977 .

[15]  Eben Matlis,et al.  Injective modules over Noetherian rings. , 1958 .

[16]  Daniel Gorenstein,et al.  An arithmetic theory of adjoint plane curves , 1952 .

[17]  L. Avramov,et al.  Factorial extensions of regular local rings and invariants of finite groups. , 1996 .

[18]  Kei-ichi Watanabe.  Certain invariant subrings are Gorenstein. II , 1974 .

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

[20]  M. Rosenlicht,et al.  Equivalence Relations on Algebraic Curves , 1952 .

[21]  Jean-Pierre Serre.  Sur la dimension homologique des anneaux et des modules noethériens , 2003 .

[22]  P. Griffith.  Normal extensions of regular local rings , 1987 .

[23]  J. Herzog,et al.  Gorenstein ideals of deviation two , 1985 .

[24]  W. Vasconcelos,et al.  On Gorenstein ideals of codimension four , 1986 .

[25]  B. Ulrich.  Gorenstein rings as specializations of unique factorization domains , 1984 .

[26]  Hyman Bass,et al.  On the ubiquity of Gorenstein rings , 1963 .

[27]  Certain invariant subrings are Gorenstein. II , 1974 .

[28]  Jean-Pierre Serre,et al.  Sur les modules projectifs , 1961 .

[29]  H. Bass.  Injective dimension in Noetherian rings , 1962 .

[30]  Joe Harris,et al.  Cayley-Bacharach theorems and conjectures , 1996 .

[31]  B. Ulrich,et al.  The structure of linkage , 1987 .

[32]  David A. Buchsbaum,et al.  Homological dimension in local rings , 1957 .

[33]  Lucien Szpiro,et al.  Liaison des variétés algébriques. I , 1974 .

[34]  R. Stanley.  Combinatorics and commutative algebra , 1983 .

[35]  Melvin Hochster,et al.  Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay , 1974 .

[36]  W. Bruns,et al.  Cohen-Macaulay rings , 1993 .

[37]  Emmy Noether.  Idealtheorie in Ringbereichen , 1921 .

[38]  David A. Buchsbaum,et al.  Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3 , 1977 .

[39]  E. Kunz.  Almost complete intersections are not Gorenstein rings , 1974 .

[40]  M. P. Murthy.  A note on factorial rings , 1964 .

[41]  E. Kunz,et al.  Der kanonische Modul eines Cohen-Macaulay-Rings , 1971 .

[42]  Friedrich Knop.  Der kanonische modul eines invariantenrings , 1989 .

[43]  P. Roberts.  Rings of Type 1 are Gorenstein , 1983 .

[44]  Ernst Kunz,et al.  Die Wertehalbgruppe eines lokalen Rings der Dimension 1 , 1971 .

[45]  R. Buchweitz,et al.  The Homological Theory of Maximal Cohen-Macaulay Approximations , 1989 .