M-hyperquasivarieties

• Autorzy: Graczyńska E. , Schweigert D.
• Języki publikacji: EN

Abstrakty

EN

We consider the notion of M-hyper-quasi-identities and M-hyperquasi-varieties, as a common generalization of the concept of quasi-identity (hyper-quasi-identity) and quasivariety (hyper-quasivariety) invented by A. I. Mal'cev, cf. [13], cf. [6] and hypervariety invented by the authors in [15], [8] and hy p erqu as i variety [9]. The results of this paper were presented on the 69th Workshop on General Algebra, held at Potsdam University (Germany) on March 18-20, 2005.

Słowa kluczowe

EN

universal algebra; algebraic systems; hyperidentities

PL

algebra uniwersalna; systemy algebraiczne; superoperatory

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 33--42
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Graczyńska E.

autor

Schweigert D.

• University of Technology Institute of Mathematics and Applications of Informatics, ul. Luboszycka 3, 45-036 Opole, Poland http://www.egracz.po.opole.pl/,

Bibliografia

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• [3] Chandrasri Chompoonut, K. Denecke, M-solid Quasivarieties, East-West J. Math. 4, No. 2 (2002), 177-190.
• [4] K. Denecke, D. Lau, R. Pöschel, and D. Schweigert, Hyperidentities, hyper- equational classes and clone congruences, Contributions to General Algebra 7, Verlag Hölder-Pichler-Tempsky, Wien 1991-Verlag B.G. Teubner, Stuttgart, (1991), 97-118.
• [5] K. Denecke, S. L. Wismath, Hyperidentities and Clones, Gordon & Breach, 2000.
• [6] V. A. Gorbunov, Algebraic Theory of Quasivarieties, Consultants Buereau 1998, New York, USA.
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• [8] E. Graczyńska and D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990), 305-318.
• [9] E. Graczyńska and D. Schweigert, Hyperquasivarieties, preprint Nr. 336, ISSN 0943-8874, August 2003, Universiatät Kaiserslautern, Germany.
• [10] E. Graczyńska and D. Schweigert, Hybrid bases for varieties of semigroups, Algebra Universalis 50 (2003), 129-139.
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• [12] D. Hobby and R. McKenzie, The Structure of Finite Algebras, AMS, vol. 76, Providence Rhode Island, USA, 1988.
• [13] A. I. Mal'cev, Algebraic Systems, Springer-Verlag, Berlin Heidelberg New York 1973.
• [14] J. Płonka, On hyperidentities of some varieties,in: Genaral Algebra and Discrete Mathematics, eds. K. Denecke, O. Lüders, Heldermann-Verlag-Berlin, 1995, pp. 199-213.
• [15] D. Schweigert, Hyperidentities, in: I. G. Rosenberg and G. Sabidussi, Algebras and Orders, 1993 Kluwer Academic Publishers, 405-506. ISBN 0-7923-2143-X. 42 E. Graczyńska, D. Schweigert
• [16] D. Schweigert, On derived varieties, Discussiones Mathematicae Algebra and Stochastic Methods 18 (1998), 17-26.
• [17] D. Schweigert, Tolerances and commutators on lattices, Bull. Austral. Math. Soc. vol 37 (1988), 213-219.