Geodesic
Free $n$-Tuple Semigroups
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 693-701.

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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, a singly generated free $n$-tuple semigroup is 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 semigroup is isomorphic to a symmetric group.
Keywords: $n$-tuple semigroup, independence of axioms, free $n$-tuple semigroup, semigroup. 
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A. V. Zhuchok. Free $n$-Tuple Semigroups. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 693-701. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a4/

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