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Idempotents, group membership and their applications

  • Štefan Porubský EMAIL logo
Veröffentlicht/Copyright: 20. November 2018
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Abstract

Š. Schwarz in his paper [SCHWARZ, Š.: Zur Theorie der Halbgruppen, Sborník prác Prírodovedeckej fakulty Slovenskej univerzity v Bratislave, Vol. VI, Bratislava, 1943, 64 pp.] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups [SCHWARZ, Š.: Contribution to the theory of torsion semigroups, Czechoslovak Math. J. 3(1) (1953), 7–21]. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory.


The author was supported by the Grant Agency of the Czech Republic, Grant # 17-02804S and the strategic development financing RVO 67985807. All computations are made using Mathematica 10 program package.


  1. Dedicated to the memory of Professor Štefan Schwarz

    (Communicated by Milan Paštéka)

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Received: 2017-08-14
Accepted: 2017-11-17
Published Online: 2018-11-20
Published in Print: 2018-12-19

© 2018 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0180/pdf
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