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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.

Congruence classes in regular varieties.

Bělohlávek, R., Chajda, I. (1999)

Acta Mathematica Universitatis Comenianae. New Series

Congruence distributivity in varieties with constants

Ivan Chajda (1986)

Archivum Mathematicum

Congruence lattices in varieties with compact intersection property

Filip Krajník, Miroslav Ploščica (2014)

Czechoslovak Mathematical Journal

We say that a variety $𝒱$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A \in 𝒱$ is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in $𝒱$ and embeddings between them. We believe that the strategy used here can...

Congruence lattices of intransitive G-Sets and flat M-Sets

Steve Seif (2013)

Commentationes Mathematicae Universitatis Carolinae

An M-Set is a unary algebra $〈 X, M 〉$ whose set $M$ of operations is a monoid of transformations of $X$ ; $〈 X, M 〉$ is a G-Set if $M$ is a group. A lattice $L$ is said to be represented by an M-Set $〈 X, M 〉$ if the congruence lattice of $〈 X, M 〉$ is isomorphic to $L$ . Given an algebraic lattice $L$ , an invariant $Π (L)$ is introduced here. $Π (L)$ provides substantial information about properties common to all representations of $L$ by intransitive G-Sets. $Π (L)$ is a sublattice of $L$ (possibly isomorphic to the trivial lattice), a $Π$ -product lattice. A $Π$ -product...

Congruence preserving operations on the ring $ℤ_{p^{3}}$

Cyril Gavala, Miroslav Ploščica, Ivana Varga (2023)

Mathematica Bohemica

We investigate the interval $I (p^{3})$ in the lattice of clones on the ring $ℤ_{p^{3}}$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.

Congruence properties of distributive double $p$ -algebras

Michael E. Adams, Rodney Beazer (1991)

Czechoslovak Mathematical Journal

Congruence relations on direct products of lattices

Jozef Pócs (1982)

Mathematica Slovaca

Congruence relations on finitary models

Ivo Rosenberg, Teo Sturm (1992)

Czechoslovak Mathematical Journal

Congruence restrictions on axes

Jaromír Duda (1992)

Mathematica Bohemica

We give Mal’cev conditions for varieties 4V4 whose congruences on the product $A \times B, A, B \in V$ , are determined by their restrictions on the axes in $A \times B$ .

Congruence schemes and their applications

Ivan Chajda, Sándor Radelecki (2005)

Commentationes Mathematicae Universitatis Carolinae

Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.

Congruence semimodularity of conservative groupoids

Ivan Chajda (1996)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Congruence submodularity

Ivan Chajda, Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.

Congruence Topologies on Universal Algebras.

Sydney Bulman-Fleming (1971)

Mathematische Zeitschrift

Congruences and homomorphisms on $Ω$ -algebras

Elijah Eghosa Edeghagba, Branimir Šešelja, Andreja Tepavčević (2017)

Kybernetika

The topic of the paper are $Ω$ -algebras, where $Ω$ is a complete lattice. In this research we deal with congruences and homomorphisms. An $Ω$ -algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an $Ω$ -valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce $Ω$ -valued congruences, corresponding quotient $Ω$ -algebras and $Ω$ -homomorphisms and we investigate connections among these notions. We prove...

Congruences and ideals in lattice effect algebras as basic algebras

Sylvia Pulmannová, Elena Vinceková (2009)

Kybernetika

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

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