Free products of n-tuple semigroups - Zhuchok, A. V.; Koppitz, J. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
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.