Direct decomposability of tolerances on lattices, semilattices and quasilattices

Congruence Lattices of Semilattices

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if 5^* is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then a...

Congruence lattices of pseudocomplemented semilattices

Congruence lattices of algebras in various varieties have been studied extensively in the literature. For example, congruence lattices (i.e. lattices of ideals) of Boolean algebras were characterized by Nachbin [18] (see also Gratzer [9] and Jonsson [16]) while congruence lattices of semilattices were investigated by Papert [19], Dean and Oehmke [4] and others. In this paper we initiate the inv...

on direct sums of baer modules

the notion of baer modules was defined recently

QUASILATTICES IN IE3 AND THEIR PROJECTION FROM LATTICES IN IEn

Congruence Lattices of Semilattices with Operators

We begin by recalling the general theory of adjoints on finite semilattices. A finite join semilattice with 0 is a lattice, with the naturally induced meet operation. Thus a finite lattice S can be regarded as a semilattice in two ways, either S = 〈S,+, 0〉 or S = 〈S,∧, 1〉. Given a (+, 0)-homomorphism g : S → T , define the adjoint h : T → S by h(t) = ∑ {s ∈ S : gs ≤ t} so that gs ≤ t iff s ≤ ht...