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. 
@article{MZM_2018_103_5_a4,
     author = {A. V. Zhuchok},
     title = {Free $n${-Tuple} {Semigroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {693--701},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a4/}
}
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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/