Green’s Relations on Submonoids of Generalized Hypersubstitutions of Type (n)
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 239-248.

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A generalized hypersubstitution of type τ = (n) is a function which takes the n-ary operation symbol f to the term of the same type σ(f) which does not necessarily preserve the arity. Let HypG(n) be the set of all these generalized hypersubstitutions of type (n). The set HypG(n) with a binary operation and the identity generalized hypersubstitution forms a monoid. The objective of this paper is to study Green’s relations on the set of all regular elements of HypG(n).
Keywords: generalized hypersubstitutions, green’s relation, regular elements
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Kunama, Pornpimol; Leeratanavalee, Sorasak. Green’s Relations on Submonoids of Generalized Hypersubstitutions of Type (n). Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 239-248. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a2/

[1] K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach Science Publishers, The Netherlands, 2000). https://doi.org/10.1201/9781482287516

[2] K. Denecke, D. Lau, R. Pöschel and D.Schweigert, Hyperidentities, Hyperequational Classes, and Clone Congruences, Contributions to General Algebra, Vol. 7 (Verlag Hölder-Pichler-Tempsky, Wien, 1991) 97–118.

[3] J.M. Howie, Fundamentals of Semigroup Theory (Oxford University Press, New York, NY, USA, 1995). https://doi.org/10.1017/S0013091500023889

[4] S. Leeratanavalee and K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, General Algebra and Applications, Proc. of the “59th Workshop on General Algebra, “15th Conference for Young Algebraists Potsdam 2000” (Shaker Verlag, 2000) 135–145.

[5] W. Puninagool and S. Leeratanavalee, Green’s relations on HypG(2), Analele stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 20 (2012) 249–264. https://doi.org/10.2478/v10309-012-0016-5

[6] W. Puninagool and S. Leeratanavalee, The monoid of generalized hypersubstitutions of type τ = (n), Discuss. Math. Gen. Alg. Appl. 30 (2010) 173–191. https://doi.org/10.7151/dmgaa.1168

[7] W. Wongpinit and S. Leeratanavalee, All maximal idempotent submonoids of HypG(n), Surveys in Math. and its Appl. 10 (2015) 41–48.