Partial actions and proper extensions of two-sided restriction semigroups

Author(s)

Dokuchaev, Mikhailo ^[1] ; Khrypchenko, Mykola ^{[2, 3]} ; Kudryavtseva, Ganna ^{[4, 5]}

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, P-2829516 Caparica - Portugal

^[4] Univ Ljubljana, Fac Civil & Geodet Engn, Jamova Cesta 2, SI-1000 Ljubljana - Slovenia

^[5] Inst Math Phys & Mech, Jadranska Ulica 19, SI-1000 Ljubljana - Slovenia

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 225, n. 9 SEP 2021.
• Web of Science Citations: 0

Abstract

We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study several classes of partial actions of two-sided restriction semigroups that generalize partial actions of monoids and of inverse semigroups. We establish an adjunction between the category P(S) of proper extensions of a restriction semigroup Sand a category A(S) of partial actions of S subject to certain conditions going back to the work of O'Carroll. In the category A(S), we specify two isomorphic subcategories, one being reflective and the other one coreflective, each of which is equivalent to the category P(S). (C) 2020 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 15/09162-9 - Non commutative algebra and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants