Algebras satisfying congruence relations

Quotient Heyting Algebras Via Fuzzy Congruence Relations

This paper aims to introduce fuzzy congruence relations over Heyting algebras (HA) and give constructions of quotient Heyting algebras induced by fuzzy congruence relations on HA. The Fuzzy First, Second and Third Isomorphism Theorems of HA are established. MSC: 06D20, 06D72, 06D75.

Congruence Lattices of Congruence Semidistributive Algebras

Nearly twenty years ago, two of the authors wrote a paper on congruence lattices of semilattices [9]. The problem of finding a really useful characterization of congruence lattices of finite semilattices seemed too hard for us, so we went on to other things. Thus when Steve Seif asked one of us at the October 1990 meeting of the AMS in Amherst what we had learned in the meantime, the answer was...

Distributive Congruence Lattices of Congruence-permutable Algebras

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

Congruence Relations on Multilattices

Extending Congruence Relations

If 91 and 23 are algebras, where 9Is23, and 6 is a congruence relation on 91, let 0® be the smallest congruence relation on 93 containing 0. 91 is called a congruence subalgebra of 93 if 9ls93 and, for every congruence relation 0 on 91, 0*n|9I|2=0. Elementary subalgebras are congruence subalgebras, and there are Directed Union and Loewenheim-Skolem Theorems for congruence subalgebras analogous ...