Structural diversity in the lattice of equational theories

This paper is principally concerned with conditions under which various partition lattices are isomorphic to intervals in either the lattice of equational theories extending a given equational theory or the lattice of subtheories of a given equational theory.

[1]  E. Nelson.  The Lattice of Equational Classes of Semigroups with Zero , 1971, Canadian Mathematical Bulletin.

[2]  George F. McNulty.  Undecidable Properties of Finite Sets of Equations , 1976, J. Symb. Log..

[3]  Stanley Burris,et al.  Lattice-theoretic decision problems in universal algebra , 1975 .

[4]  Bjarni Jónsson,et al.  Relatively free proucts in regular varieties , 1974 .

[5]  R. P. Dilworth.  Review: G. Birkhoff, Lattice theory , 1950 .

[6]  Local Malcev Conditions , 1972, Canadian Mathematical Bulletin.

[7]  Identities in finite partition lattices , 1961 .

[8]  J. Gerhard,et al.  The lattice of equational classes of idempotent semigroups , 1970 .

[9]  Sums of finitely based lattice varieties , 1974 .

[10]  K. A. Baker.  Equational axioms for classes of lattices , 1971 .

[11]  G. McNulty.  Covering in the lattice of equational theories and some properties of term finite theories , 1982 .

[12]  P. M. Whitman,et al.  Lattices, equivalence relations, and subgroups , 1946 .

[13]  Ralph Freese.  The Structure of Modular Lattices of Width Four , 1977 .

[14]  Charles Frederick Fennemore,et al.  All varieties of bands , 1970 .

[15]  George F. McNulty,et al.  The decision problem for equational bases of algebras , 1976 .

[16]  George Gratzer,et al.  Universal Algebra , 1979 .

[17]  Ralph McKenzie.  Equational Bases for Lattice Theories. , 1970 .

[18]  Jan Kalicki.  The number of equationally complete classes of equations , 1955 .

[19]  W. Taylor.  Equational logic , 1979 .

[20]  Walter Taylor,et al.  Characterizing Mal’cev conditions , 1973 .

[21]  Stanley Burris,et al.  Embedding the dual ofΠ∞ in the lattice of equational classes of semigroups , 1971 .

[22]  Dana Scott,et al.  Equationally Complete Extensions of Finite Algebras , 1956 .

[23]  H. Neumann.  Varieties of Groups , 1967 .

[24]  Jaroslav Ježek.  Primitive classes of algebras with unary and nullary operations , 1969 .

[25]  Peter Perkins.  Bases for equational theories of semigroups , 1969 .

[26]  J. Ježek.  Intervals in the lattice of varieties , 1976 .

[27]  Stanley Burris,et al.  Embedding the dual of _{} in the lattice of equational classes of commutative semigroups , 1971 .

[28]  Equational classes of modular lattices , 1969 .

[29]  Trevor Evans,et al.  The lattice of semigroup varieties , 1971 .

[30]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[31]  Alfred Tarski,et al.  Equational Logic and Equational Theories of Algebras , 1968 .

[32]  E. Nelson.  The Lattice of Equational Classes of Commutative Semigroups , 1971, Canadian Journal of Mathematics.

[33]  The Ascending and Descending Varietal Chains of a Variety , 1975, Canadian Journal of Mathematics.

[34]  Eugene Jacobs,et al.  The Lattice of Equational Classes of Algebras with One Unary Operation , 1964 .