Congruence-semimodular and congruence-distributive pseudocomplemented semilattices
نویسندگان
چکیده
منابع مشابه
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...
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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...
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This paper continues the examination of the structure of pseudocomplemented distributive lattices. First, the Congruence Extension Property is proved. This is then applied to examine properties of the equational classes ¿Sn, — lá«So), which is a complete list of all the equational classes of pseudocomplemented distributive lattices (see Part I). The standard semigroups (i.e., the semigroup gene...
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ژورنال
عنوان ژورنال: Algebra Universalis
سال: 1982
ISSN: 0002-5240,1420-8911
DOI: 10.1007/bf02483909