(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup

(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup

We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.

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Veröffentlicht in:Categories and General Algebraic Structures with Applications 2021-07, Vol.15 (1), p.255-272
1. Verfasser: MARY, Xavier
Format: Artikel
Sprache:eng
Schlagworte:
generalized inverses
green’s relations
Group Theory
Mathematics
reverse order law
Rings and Algebras
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Beschreibung
Zusammenfassung:We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.
ISSN:2345-5853
2345-5861
2345-5861
DOI:10.52547/cgasa.15.1.255