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Congruences on pseudocomplemented semilattices

Zuzana Heleyová (2000)

Discussiones Mathematicae - General Algebra and Applications

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 to a more...

Congruences on semilattices with section antitone involutions

Ivan Chajda (2010)

Discussiones Mathematicae - General Algebra and Applications

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.

Conjugated algebras

Ivan Chajda (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone...

Construction du treillis de Galois d'une relation binaire

A. Guénoche (1990)

Mathématiques et Sciences Humaines

Cet article constitue une présentation unifiée des principales méthodes de construction du treillis de Galois d'une correspondance. Nous rappelons d'abord sa définition, puis nous décrivons quatre algorithmes de construction des éléments du treillis qui sont les rectangles maximaux de la relation binaire. Ces algorithmes ne sont pas originaux. Les descriptions précises de algorithmes, le plus souvent absentes des publications originales, permettent une programmation simple, dans un langage procédural...

Convex isomorphic ordered sets

Petr Emanovský (1993)

Mathematica Bohemica

V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered...

Convex isomorphism of Q -lattices

Petr Emanovský (1993)

Mathematica Bohemica

V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the q -lattices defined in [2] and to characterize the convex isomorphic q -lattices.

Convex isomorphisms of directed multilattices

Ján Jakubík, Mária Csontóová (1993)

Mathematica Bohemica

By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.

Convexity in subsets of lattices.

Sergei V. Ovchinnikov (1980)

Stochastica

The notion of convex set for subsets of lattices in one particular case was introduced in [1], where it was used to study Paretto's principle in the theory of group choice. This notion is based on a betweenness relation due to Glivenko [2]. Betweenness is used very widely in lattice theory as basis for lattice geometry (see [3], and, especially [4 part 1]).In the present paper the relative notions of convexity are considered for subsets of an arbitrary lattice.In section 1 certain relative notions...

Countable 1-transitive coloured linear orderings II

G. Campero-Arena, J. K. Truss (2004)

Fundamenta Mathematicae

This paper gives a structure theorem for the class of countable 1-transitive coloured linear orderings for a countably infinite colour set, concluding the work begun in [1]. There we gave a complete classification of these orders for finite colour sets, of which there are ℵ₁. For infinite colour sets, the details are considerably more complicated, but many features from [1] occur here too, in more marked form, principally the use (now essential it seems) of coding trees, as a means of describing...

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