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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03 October 2019
1) The affiliation of the first author should read Taras Shevchenko Luhansk National University, Starobilsk, Ukraine.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 11, pp. 1484–1498, November, 2018.
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Zhuchok, A., Koppitz, J. Free Products of n-Tuple Semigroups. Ukr Math J 70, 1710–1726 (2019). https://doi.org/10.1007/s11253-019-01601-2
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DOI: https://doi.org/10.1007/s11253-019-01601-2