Displaying similar documents to “Congruences on pseudocomplemented semilattices”

Lattices and semilattices having an antitone involution in every upper interval

Ivan Chajda (2003)

Commentationes Mathematicae Universitatis Carolinae

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We study ∨ -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.

Congruence classes in Brouwerian semilattices

Ivan Chajda, Helmut Länger (2001)

Discussiones Mathematicae - General Algebra and Applications

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Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.

Subdirectly irreducible sectionally pseudocomplemented semilattices

Radomír Halaš, Jan Kühr (2007)

Czechoslovak Mathematical Journal

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Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...

Congruence kernels of distributive PJP-semilattices

S. N. Begum, Abu Saleh Abdun Noor (2011)

Mathematica Bohemica

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A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.