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Matematicheskie Zametki, 2018, Volume 103, Issue 5, Pages 693–701
DOI: https://doi.org/10.4213/mzm11324 (Mi mzm11324) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Free $n$-Tuple Semigroups

A. V. Zhuchok

Lugansk Taras Shevchenko National University
Full-text PDF (456 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm11324
Abstract: The present paper is devoted to the study of $n$-tuple semigroups. A free $n$-tuple semigroup of arbitrary rank is constructed and, as a consequence, a singly generated free $n$-tuple semigroup is characterized. Moreover, examples of $n$-tuple semigroups are presented, the independence of the $n$-tuple semigroup axioms is proved, and it is shown that the natural semigroups of the constructed free $n$-tuple semigroup are isomorphic and the automorphism group of this semigroup is isomorphic to a symmetric group.
Keywords: $n$-tuple semigroup, independence of axioms, free $n$-tuple semigroup, semigroup.
Received: 21.07.2016
Revised: 27.02.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 737–744
DOI: https://doi.org/10.1134/S0001434618050061
Bibliographic databases:
Document Type: Article
UDC: 512.579
Language: Russian
Citation: A. V. Zhuchok, “Free $n$-Tuple Semigroups”, Mat. Zametki, 103:5 (2018), 693–701; Math. Notes, 103:5 (2018), 737–744
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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