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Idempotents, group membership and their applications

In: Mathematica Slovaca, vol. 68, no. 6
Štefan Porubský
Rok, strany: 2018, 1231 - 1312
Kľúčové slová:
multiplicative semigroup, finite semigroups, power semigroups, idempotent elements, finite commutative rings, principal ideal domain, Euler-Fermat theorem, Wilson theorem, matrices over fields
O článku:
Š. Schwarz in his paper [SCHWARZ, Š.: \textit{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.: \textit{Contribution to the theory of torsion semigroups}, Czechoslovak Math. J. \textbf{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.
Ako citovať:
ISO 690:
Porubský, Š. 2018. Idempotents, group membership and their applications. In Mathematica Slovaca, vol. 68, no.6, pp. 1231-1312. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0180

Porubský, Š. (2018). Idempotents, group membership and their applications. Mathematica Slovaca, 68(6), 1231-1312. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0180
O vydaní:
Publikované: 3. 12. 2018