Free Products of n-Tuple Semigroups

  • A.V. Zhuchok
  • J. Koppitz

We construct a free product of arbitrary n-tuple semigroups, introduce the notion of n-bands 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 any rank and characterize one-generated free commutative n-tuple semigroups. Moreover, we describe the least commutative congruence on a free n-tuple semigroup and prove that the semigroups of the constructed free commutative n-tuple semigroup are isomorphic and that its automorphism group is isomorphic to a symmetric group.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A.V. Zhuchok
    • 1
  • J. Koppitz
    • 2
  1. 1.T. Shevchenko Lugansk National UniversityLuganskUkraine
  2. 2.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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