Free products of $n$-tuple semigroups

  • A. V. Zhuchok Київ. нац. ун-т їм. T. Шевченка
  • J. Koppitz


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.
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,
Research articles