Binary relations on the monoid of V-proper hypersubstitutions

• Autorzy: Klaus Denecke , Rattana Srithus
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.

Słowa kluczowe

EN

solid variety; degree of proper hypersubstitutions; isomorphism degree of proper hypersubstitutions

Kategorie tematyczne

• 08B15: Lattices of varieties
• 20M07: Varieties and pseudovarieties of semigroups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 233-251

Daty

wydano

2006

otrzymano

2006-10-26

poprawiono

2006-11-06

Twórcy

autor

Klaus Denecke

• Universität Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Rattana Srithus

• Universität Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

Bibliografia

• [1] St. Burris and H.P. Sankappanavar, A course in Universal Algebra, Springer-Verlag, New York, Heidelberg, Berlin 1981.
• [2] K. Denecke and J. Koppitz, Fluid, unsolid, and completely unsolid varieties, Algebra Colloquium 7:4 (2000), 381-390.
• [3] K. Denecke and R. Marszałek, Binary Relations on Monoids of Hypersubstitutions, Algebra Colloquium 4:1 (1997), 49-64.
• [4] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Science Publishers, 2000.
• [5] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Boca Raton, London, Washington, D.C.: Chapman & Hall/CRC 2002.
• [6] K. Denecke, J. Koppitz and R. Srithus, The Degree of Proper Hypersubstitutions, preprint 2005.
• [7] K. Denecke, J. Koppitz and R. Srithus, N-fluid Varieties, preprint 2005.
• [8] E. Graczyńska, M-solid Quasivarieties, preprint 2006.
• [9] E. Graczyńska and D. Schweigert, The Dimension of a Variety, preprint 2006.
• [10] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2006.
• [11] J. Płonka, Proper and inner hypersubstitutions of varieties, p. 106-116 in: 'Proceedings of the International Conference Sommer School on General Algebra and Ordered Sets', Olomouc 1994.

Identyfikatory

DOI

10.7151/dmgaa.1114