Displaying similar documents to “Congruence classes in Brouwerian semilattices”

Congruences on pseudocomplemented semilattices

Zuzana Heleyová (2000)

Discussiones Mathematicae - General Algebra and Applications

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It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B₁ [5]. In this paper we give a partial solution...

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.

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...

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.

Congruences on semilattices with section antitone involutions

Ivan Chajda (2010)

Discussiones Mathematicae - General Algebra and Applications

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We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.