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( L , ϕ ) -representations of algebras

Andrzej Walendziak (1993)

Archivum Mathematicum

In this paper we introduce the concept of an ( L , ϕ ) -representation of an algebra A which is a common generalization of subdirect, full subdirect and weak direct representation of A . Here we characterize such representations in terms of congruence relations.

A note on triangular schemes for weak congruences

Ivan Chajda, Branimir Šešelja, Andreja Tepavčević (2005)

Czechoslovak Mathematical Journal

Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity.

Abelian differential modes are quasi-affine

David Stanovský (2012)

Commentationes Mathematicae Universitatis Carolinae

We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings.

All completely regular elements in H y p G ( n )

Ampika Boonmee, Sorasak Leeratanavalee (2013)

Discussiones Mathematicae - General Algebra and Applications

In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties. Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In...

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