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The Shape of Congruence Lattices
Introduction Preliminary notions Strong term conditions Meet continuous congruence identities Rectangulation A theory of solvability Ordinary congruence identities Congruence meet and joinExpand
Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties
We show that the class of locally finite varieties omitting type 1 has the following properties. This class is:(1)definable by an idempotent, linear, strong Mal’cev condition in a language with oneExpand
The Relationship Between Two Commutators
It is derived that if A is an abelian algebra and (A) satisfies an idempotent Mal'cev condition which fails to hold in the variety of semilattices, then A is affine, and it is refined by showing that abelIAN algebras are quasi-affine in such varieties. Expand
Congruence modular varieties with small free spectra
Abstract. Let A be a finite algebra that generates a congruence modular variety. We show that the free spectrum of ${\cal V}({\bf A})$ fails to have a doubly exponentially lower bound if and only ifExpand
An Order-Theoretic Property of the Commutator
  • K. Kearnes
  • Mathematics, Computer Science
  • Int. J. Algebra Comput.
  • 1 December 1993
It is shown that any solvable E-minimal algebra is leftnilpotent, any finite algebra whose congruence lattice contains a 0, 1-sublattice isomorphic to M3 is left nilpotent and any homomorphic image of a finite abeliangebra is left and right nilpotents. Expand
Semilattice modes I: the associated semiring
We examine idempotent, entropic algebras (modes) which have a semilattice term. We are able to show that any variety of semilattice modes has the congruence extension property and is residuallyExpand
An easy test for congruence modularity
We describe an easy way to determine whether the realization of a set of idempotent identities guarantees congruence modularity or the satisfaction of a nontrivial congruence identity. Our resultsExpand
Clones of finite groups
Abstract.If G is a finite group whose Sylow subgroups are abelian, then the term operations of G are determined by the subgroups of G × G × G.
Commutator theory for relatively modular quasivarieties
We develop a commutator theory for relatively modular quasivarieties that extends the theory for modular varieties. We characterize relatively modular quasivarieties, prove that they have anExpand
Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound
We show that a residually finite, congruence meet-semidistributive variety of finite type is residually < N for some finite N . This solves Pixley’s problem and a special case of the restrictedExpand