Globalization of partial actions of semigroups

Kudryavtseva, Ganna (author), Laan, Valdis (author)

We propose two universal constructions of globalization of a partial action of a semigroup on a set, satisfying certain conditions which arise in Morita theory of semigroups. One of the constructions is based on the tensor product of a partial semigroup act with the semigroup and generalizes the globalization construction of strong partial actions of monoids due to Megrelishvili and Schröder. It produces the initial object in an appropriate category of globalizations of a given partial action. The other construction involves Hom-sets and is novel even in the monoid setting. It produces the terminal object in an appropriate category of globalizations. While in the group case the results of the two constructions are isomorphic, they can be far different in the monoid case.

• Language: English
• Keywords: partial action, partial semigroup action, partial monoid action, globalization, enveloping action
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 200-217
• Numbering: Vol. 107, iss. 1
• PID: 20.500.12556/RUL-151958
• UDC: 512.53
• ISSN on article: 0037-1912
• DOI: 10.1007/s00233-023-10364-z
• COBISS.SI-ID: 155578883
• Publication date in RUL: 26.10.2023

Record is a part of a journal

• Title: Semigroup forum
• Publisher: Springer Nature
• ISSN: 0037-1912
• COBISS.SI-ID: 26378752

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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