Abstract
The present paper is devoted to the study of n-tuple semigroups. A free n-tuple semigroup of arbitrary rank is constructed and, as a consequence, singly generated free n-tuple semigroups are characterized. Moreover, examples of n-tuple semigroups are presented, the independence of the n-tuple semigroup axioms is proved, and it is shown that the natural semigroups of the constructed free n-tuple semigroup are isomorphic and the automorphism group of this n-tuple semigroup is isomorphic to a symmetric group.
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Original Russian Text © A. V. Zhuchok, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 5, pp. 693–701.
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Zhuchok, A.V. Free n-Tuple Semigroups. Math Notes 103, 737–744 (2018). https://doi.org/10.1134/S0001434618050061
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DOI: https://doi.org/10.1134/S0001434618050061