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, 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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