Název: Idempotents, Group Membership and their Applications
Autoři: Porubský, Štefan
Typ dokumentu: Výzkumné zprávy
Rok: 2017
Jazyk: eng
Edice: Technical Report, svazek: V-1248
Abstrakt: 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.
Klíčová slova: 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
Číslo projektu: GA17-02804S (CEP)
Poskytovatel projektu: GA ČR

Instituce: Ústav informatiky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný na vyžádání prostřednictvím repozitáře Akademie věd.
Původní záznam: http://hdl.handle.net/11104/0273447

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-361693


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