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$𝔄 (1, 1)$ can be strongly embedded into category of semigroups

Jiří Sichler (1968)

Commentationes Mathematicae Universitatis Carolinae

$(L, ϕ)$ -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.

$(ℒ$ , $ℒ^{'})$ -products of algebras

Andrzej Walendziak (1998)

Mathematica Slovaca

$𝒬$ -универсальные квазимогообразия графов.

А.В. Кравченко (2002)

Algebra i Logika

0-conditions and tolerance schemes.

Chajda, I., Radeleczki, S. (2003)

Acta Mathematica Universitatis Comenianae. New Series

2-normalization of lattices

Ivan Chajda, W. Cheng, S. L. Wismath (2008)

Czechoslovak Mathematical Journal

Let $τ$ be a type of algebras. A valuation of terms of type $τ$ is a function $v$ assigning to each term $t$ of type $τ$ a value $v (t) \geq 0$ . For $k \geq 1$ , an identity $s \approx t$ of type $τ$ is said to be $k$ -normal (with respect to valuation $v$ ) if either $s = t$ or both $s$ and $t$ have value $\geq k$ . Taking $k = 1$ with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called $k$ -normal (with respect to the valuation $v$ ) if all its identities are $k$ -normal. For any variety $V$ , there is a least...