Congruence lattices of semilattices
نویسندگان
چکیده
منابع مشابه
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...
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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...
متن کاملCongruence 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...
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We show that for every quasivariety K of relational structures there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0, F). It is known that if S is a join semilattice with 0, then there is a quasivariety Q such that the lattice of theories of Q is isomorphic to Con(S,+, 0) (w...
متن کاملLattices of Quasi-Equational Theories as Congruence Lattices of Semilattices with Operators: Part II
Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0,F). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety Q such that ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1973
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1973.49.51