Polycyclic extensions of semigroups

DOI10.30970/VMM.2020.90.020-047zbMATH Open1499.20141arXiv2107.14408OpenAlexW4206800992MaRDI QIDQ3390893

Pavlo Khylynskyi, Oleg Gutik

Publication date: 25 March 2022

Published in: Visnyk L'vivs'kogo Universytetu. Seriya Mekhaniko-Matematychna (Search for Journal in Brave)

Abstract: In the paper we introduce a notion of the Bruck-Reilly $lambda$-polycyclic extension of a monoid $S$ with a homomorphism $heta$ which is an analogue of the Bruck-Reilly extension of a monoid $S$. We describe idempotens of the semigroup $left(mathscr{P}_{lambda}(heta,S),*ight)$ and Green's relations on $left(mathscr{P}_{lambda}(heta,S),*ight)$. It is proved that $left(mathscr{P}_{lambda}(heta,S),*ight)$ is a $0$-simple semigroup for any semigroup $S$. We find necessary and sufficient conditions on a monoid $S$ and a homomorphism $heta$ under which the semigroup $left(mathscr{P}_{lambda}(heta,S),*ight)$ is regular, inverse, $0$-bisimple, combinatorial, congruence free, or inverse 0-E-unitary. Also we study topologizations of the semigroup $left(mathscr{P}_{lambda}(heta,S),*ight)$.

Full work available at URL: https://arxiv.org/abs/2107.14408

zbMATH Keywords

semigroupsemitopological semigrouptopological semigroupextensionpolycyclic monoid

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Structure of topological semigroups (22A15) Mappings of semigroups (20M15) Connections of semigroups with homological algebra and category theory (20M50)

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