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Displaying 41 – 54 of 54

Congruences and ideals in ternary rings

Ivan Chajda, Radomír Halaš, František Machala (1997)

Czechoslovak Mathematical Journal

A ternary ring is an algebraic structure $ℛ = (R; t, 0, 1)$ of type $(3, 0, 0)$ satisfying the identities $t (0, x, y) = y = t (x, 0, y)$ and $t (1, x, 0) = x = (x, 1, 0)$ where, moreover, for any $a$ , $b$ , $c \in R$ there exists a unique $d \in R$ with $t (a, b, d) = c$ . A congruence $θ$ on $ℛ$ is called normal if $ℛ / θ$ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on $ℛ$ and establish connections between ideals (introduced earlier by the third author) and congruence kernels.

Congruences and ideals on left divisible involutory groupoids

Radomír Halaš (1996)

Mathematica Bohemica

In [1] ideals and congruences on semiloops were investigated. The aim of this paper is to generalize results obtained for semiloops to the case of left divisible involutory groupoids.

Congruences associated with inverse transversals.

T. S. Blyth, M. H. Almeida Santos (1995)

Collectanea Mathematica

Congruences generated by filters

Jaromír Duda (1980)

Commentationes Mathematicae Universitatis Carolinae

Congruences of pseudocomplemented algebras

Prata dos Santos, R. (1983/1984)

Portugaliae mathematica

Congruences on an inverse Bruck-Reilly monoid. Part I: Non-group congruences.

S.A. Rankin (1991)

Semigroup forum

Congruences on bands of π-groups

Sunil K. Maity (2013)

Discussiones Mathematicae - General Algebra and Applications

A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.

Congruences on Bruck-Reilly extensions of monoids.

B. Piochi (1995)

Semigroup forum

Congruences on products in varieties satisfying the CEP

Jaromír Duda (1986)

Mathematica Slovaca

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.

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