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Some modifications of congruence permutability and dually congruence regular varietie

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Chajda I., Eigenthaler G.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 2

165-174

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].

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Chajda I.

1 Eigenthaler G.

1 2001

Wyniki wyszukiwania

Some modifications of congruence permutability and dually congruence regular varietie