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2001 | 21 | 2 | 165-174
Tytuł artykułu

Some modifications of congruence permutability and dually congruence regular varietie

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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].
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autor
  • Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, CZ-77900 Olomouc, Czech Republic
  • Institut für Algebra und Computermathematik, Technische Universität Wien, Wiedner Hauptstraß e 8-10, A-1040 Wien, Austria
Bibliografia
  • [1] G.D. Barbour and J.G. Raftery, On the degrees of permutability of subregular varieties, Czechoslovak Math. J. 47 (1997), 317-325.
  • [2] R. Belohlávek and I. Chajda, Congruence classes in regular varieties, Acta Math. Univ. Com. (Bratislava) 68 (1999), 71-76.
  • [3] I. Chajda, Locally regular varieties, Acta Sci. Math. (Szeged) 64 (1998), 431-435.
  • [4] I. Chajda, Semi-implication algebras, Tatra Mt. Math. Publ. 5 (1995), 13-24.
  • [5] I. Chajda, Normally presented varieties, Algebra Universalis 34 (1995), 327-335.
  • [6] I. Chajda and G. Eigenthaler, Dually regular varieties, Contributions to General Algebra 12 (2000), 121-128.
  • [7] I. Chajda and H. Länger, Ring-like operations in pseudocomplemented semilattices, Discuss. Math. Gen. Algebra Appl. 20 (2000), 87-95.
  • [8] E. Graczyńska, On normal and regular identities, Algebra Universalis 27 (1990), 387-397.
  • [9] J. Hagemann and A. Mitschke, On n-permutable congruences, Algebra Universalis 3 (1973), 8-12.
  • [10] A.I. Mal'cev, On the general theory of algebraic systems (Russian), Mat. Sbornik 35 (1954), 8-20.
  • [11] I.I. Melnik, Nilpotent shifts of varieties (Russian), Mat. Zametki 14 (1973), 703-712.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1035
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