Original title: Idempotents, Group Membership and their Applications
Authors: Porubský, Štefan
Document type: Research reports
Year: 2017
Language: eng
Series: Technical Report, volume: V-1248
Abstract: S.Schwarz in his paper [165] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought [167] into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups. 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.
Keywords: Euler-Fermat theorem; finite commutative rings; finite semigroups; idempotent elements; matrices over fields; maximal groups contained in a semigroup; multiplicative semigroup; multiplicative semigroup of Zm; periodic sequence; power semigroups; principal ideal domain; semigroup of circulant Boolean matrices; Wilson theorem
Project no.: GA17-02804S (CEP)
Funding provider: GA ČR

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0273447

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