Free products of $n$-tuple semigroups
AbstractWe 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.
How to Cite
Zhuchok, A. V., and J. Koppitz. “Free Products of $n$-Tuple Semigroups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 11, Nov. 2018, pp. 1484-98, http://umj.imath.kiev.ua/index.php/umj/article/view/1652.