Discussiones
Mathematicae General Algebra and Applications 20(2) (2000) 183-192
DOI: https://doi.org/10.7151/dmgaa.1015
THE ORDER OF NORMAL FORM HYPERSUBSTITUTIONS OF TYPE (2)
Klaus Denecke University of Potsdam, Institute of Mathematics |
Kazem Mahdavi State University of New York, College at Potsdam |
Abstract
In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
Keywords: hypersubstitutions, terms, idempotent elements, elements of infinite order.
1991 Mathematics Subject Classification: Primary 20M14; Secondary 20M07, 08A40.
References
| [1] | K. Denecke, D. Lau, R. Pöschel, and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contributions to General Algebra 7 (1991), 97-118. |
| [2] | K. Denecke and Sh. Wismath, The Monoid of Hypersubstitutions of Type (2), Contributions to General Algebra, Verlag Johannes Heyn, 10 (1998), 110-126. |
| [3] | K. Denecke and Sh. Wismath, "Hyperidentities and clones," Gordon and Breach Sci. Publ., Amsterdam-Singapore 2000. |
| [4] | J. P onka, Proper and inner hypersubstitutions of varieties, p. 106-115 in: ``Proceedings of the International Conference: Summer school on General Algebra and Ordered sets 1994'', Palacký University, Olomouc 1994. |
Received 3 December 1997
Revised 30 December 1999
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