DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

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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
PF 60 15 53, 14415 Potsdam, Germany
e-mail: kdenecke@rz.uni-potsdam.de

Kazem Mahdavi

State University of New York, College at Potsdam
Department of Mathematics
Potsdam, NY 13767, USA

e:mail mahdavk@potsdam.edu

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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