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].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1015,
author = {Klaus Denecke and Kazem Mahdavi},
title = {The order of normalform hypersubstitutions of type (2)},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {183-192},
zbl = {0982.20044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1015}
}
Klaus Denecke; Kazem Mahdavi. The order of normalform hypersubstitutions of type (2). Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 183-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1015/
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[001] [2] K. Denecke and Sh. Wismath, The Monoid of Hypersubstitutions of Type (2), Contributions to General Algebra, Verlag Johannes Heyn, 10 (1998), 110-126. | Zbl 1080.20503
[002] [3] K. Denecke and Sh. Wismath, 'Hyperidentities and clones', Gordon and Breach Sci. Publ., Amsterdam-Singapore 2000.
[003] [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. | Zbl 0828.08003