Geodesic
The order of normalform hypersubstitutions of type (2)
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 183-192.

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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].
Keywords: hypersubstitutions, terms, idempotent elements, elements of infinite order 
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Denecke, Klaus; Mahdavi, Kazem. The order of normalform hypersubstitutions of type (2). Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 183-192. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_2_a2/

[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. 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.