Free n-Tuple Semigroups
Anatolii V. Zhuchok · Mathematical Notes · 2018
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.