Some modifications of congruence permutability and dually congruence regular varietie

Ivan Chajda, and Günther Eigenthaler. "Some modifications of congruence permutability and dually congruence regular varietie." Discussiones Mathematicae - General Algebra and Applications 21.2 (2001): 165-174. <http://eudml.org/doc/287616>.

@article{IvanChajda2001,
abstract = {It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity with respect to a unary term g". The natural problem arises what modification of n-permutability is satisfied by dually congruence regular varieties. The aim of this paper is to find out such a modification, to characterize varieties satisfying it by a Mal'cev type condition and to show connections with normally presented varieties (see e.g. [5], [8], [11]). The latter concept was introduced already by J. P≥onka under a different term; the names "normal identity" and "normal variety" were firstly used by E. Graczyńska in [8].},
author = {Ivan Chajda, Günther Eigenthaler},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {congruence regularity; local congruence regularity; dual congruence regularity; local n-permutability; dually congruence regular varieties; locally n-permutable at a unary term; Mal'tsev type characterization; normal variety; normal closure of a variety; dually congruence regular algebras},
language = {eng},
number = {2},
pages = {165-174},
title = {Some modifications of congruence permutability and dually congruence regular varietie},
url = {http://eudml.org/doc/287616},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Ivan Chajda
AU - Günther Eigenthaler
TI - Some modifications of congruence permutability and dually congruence regular varietie
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 2
SP - 165
EP - 174
AB - It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity with respect to a unary term g". The natural problem arises what modification of n-permutability is satisfied by dually congruence regular varieties. The aim of this paper is to find out such a modification, to characterize varieties satisfying it by a Mal'cev type condition and to show connections with normally presented varieties (see e.g. [5], [8], [11]). The latter concept was introduced already by J. P≥onka under a different term; the names "normal identity" and "normal variety" were firstly used by E. Graczyńska in [8].
LA - eng
KW - congruence regularity; local congruence regularity; dual congruence regularity; local n-permutability; dually congruence regular varieties; locally n-permutable at a unary term; Mal'tsev type characterization; normal variety; normal closure of a variety; dually congruence regular algebras
UR - http://eudml.org/doc/287616
ER -