Free products of $n$-tuple semigroups
We construct a free product of arbitrary n-tuple semigroups, introduce the notion of $n$-band of $n$-tuple semigroups and, in terms of this notion, describe the structure of the free product. We also construct a free commutative $n$-tuple semigroup of an arbitrary rank and characterize one-generated free commutative $n$-tuple semigroups. Moreover, we describe the least commutative congruence on a free $n$-tuple semigroup and establish that the semigroups of the constructed free commutative $n$-tuple semigroup are isomorphic and its automorphism group is isomorphic to the symmetric group.
Citation Example: Koppitz J., Zhuchok A. V. Free products of $n$-tuple semigroups // Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1484-1498.