Some modifications of congruence permutability and dually congruence regular varietie
Treść / Zawartość
It is well known that every congruence regular variety is n-permutable (in the sense of ) for some n ≥ 2. For the explicit proof see e.g. . The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery . The concept of local congruence regularity was introduced in . A common generalization of congruence regularity and local congruence regularity was given in  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. , , ). 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 .
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