Discussiones Mathematicae General Algebra and Applications 21(2) (2001) 165-174
doi: 10.7151/dmgaa.1035

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SOME MODIFICATIONS OF CONGRUENCE PERMUTABILITY AND DUALLY CONGRUENCE REGULAR VARIETIE

Ivan Chajda

Department of Algebra and Geometry
Palacký University of Olomouc
Tomkova 40, CZ-77900 Olomouc, Czech Republic
e-mail: chajda@risc.upol.cz

Günther Eigenthaler

Institut für Algebra und Computermathematik
Technische Universität Wien
Wiedner Hauptstraß e 8-10, A-1040 Wien, Austria
e-mail:
g.eigenthaler@tuwien.ac.at

Abstract

It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ł 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. Płonka under a different term; the names "normal identity" and "normal variety" were firstly used by E. Graczyńska in [8].

Keywords: congruence regularity, local congruence regularity, dual congruence regularity, local n-permutability.

2000 Mathematics Subject Classification: Primary 08A30, Secondary 08B05.

References

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Received 18 December 2000
Revised 6 June 2001