The order of normalform hypersubstitutions of type (2)

Klaus Denecke; Kazem Mahdavi

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 183-192
  • ISSN: 1509-9415

Abstract

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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].

How to cite

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Klaus Denecke, and Kazem Mahdavi. "The order of normalform hypersubstitutions of type (2)." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 183-192. <http://eudml.org/doc/287741>.

@article{KlausDenecke2000,
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].},
author = {Klaus Denecke, Kazem Mahdavi},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hypersubstitutions; terms; idempotent elements; elements of infinite order; hypersubstitutions of finite order; varieties of semigroups; hyperidentities; normal forms},
language = {eng},
number = {2},
pages = {183-192},
title = {The order of normalform hypersubstitutions of type (2)},
url = {http://eudml.org/doc/287741},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Klaus Denecke
AU - Kazem Mahdavi
TI - The order of normalform hypersubstitutions of type (2)
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 183
EP - 192
AB - 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].
LA - eng
KW - hypersubstitutions; terms; idempotent elements; elements of infinite order; hypersubstitutions of finite order; varieties of semigroups; hyperidentities; normal forms
UR - http://eudml.org/doc/287741
ER -

References

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  1. [1] K. Denecke, D. Lau, R. Pöschel, and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contributions to General Algebra 7 (1991), 97-118. Zbl0759.08005
  2. [2] K. Denecke and Sh. Wismath, The Monoid of Hypersubstitutions of Type (2), Contributions to General Algebra, Verlag Johannes Heyn, 10 (1998), 110-126. Zbl1080.20503
  3. [3] K. Denecke and Sh. Wismath, 'Hyperidentities and clones', Gordon and Breach Sci. Publ., Amsterdam-Singapore 2000. 
  4. [4] J. Płonka, Proper and inner hypersubstitutions of varieties, 'Proceedings of the International Conference: Summer school on General Algebra and Ordered sets 1994', Palacký University, Olomouc 1994, 106-115. Zbl0828.08003

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