@article{90e261c5f4fb4789a2127de643e03660,

title = "Partial actions and proper extensions of two-sided restriction semigroups",

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 S and 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).",

keywords = "Expansion, Inverse monoid, Partial action, Prefix group expansion, Premorphism, Restriction monoid",

author = "Mikhailo Dokuchaev and Mykola Khrypchenko and Ganna Kudryavtseva",

note = "Funding Information: The work on this paper began during the visits of the first author (in January 2017) and of the second author (in January 2017, February 2018 and February 2019) to the Institute of Mathematics, Physics and Mechanics (IMFM) of Ljubljana, some of which were partially supported by ARRS grant P1-0288 . The first author was partially supported by FAPESP of Brazil (Process 2015/09162-9 ) and by CNPq of Brazil (Process 307873/2017-0 ). The second author was partially supported by CNPq of Brazil (Process 404649/2018-1 ) and by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PTDC/MAT-PUR/31174/2017 . The third author was partially supported by ARRS grant P1-0288 . Funding Information: The work on this paper began during the visits of the first author (in January 2017) and of the second author (in January 2017, February 2018 and February 2019) to the Institute of Mathematics, Physics and Mechanics (IMFM) of Ljubljana, some of which were partially supported by ARRS grant P1-0288. The first author was partially supported by FAPESP of Brazil (Process 2015/09162-9) and by CNPq of Brazil (Process 307873/2017-0). The second author was partially supported by CNPq of Brazil (Process 404649/2018-1) and by the Funda??o para a Ci?ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PTDC/MAT-PUR/31174/2017. The third author was partially supported by ARRS grant P1-0288. We thank the referee for a very careful reading of the paper and a number of valuable comments and suggestions. Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2021",

month = sep,

doi = "10.1016/j.jpaa.2020.106649",

language = "English",

volume = "225",

journal = "Journal Of Pure And Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier Science B.V., Amsterdam.",

number = "9",

}