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Globalization of partial actions of semigroups
ID
Kudryavtseva, Ganna
(
Author
),
ID
Laan, Valdis
(
Author
)
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MD5: C281044F616782C3177315501B9E7143
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https://link.springer.com/article/10.1007/s00233-023-10364-z
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Abstract
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
Views:
425
Downloads:
37
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Record is a part of a journal
Title:
Semigroup forum
Publisher:
Springer Nature
ISSN:
0037-1912
COBISS.SI-ID:
26378752
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Projects
Funder:
ARRS - Slovenian Research Agency
Project number:
BI-EE/20-22-010
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0288
Name:
Algebra in njena uporaba
Funder:
Other - Other funder or multiple funders
Funding programme:
Estonian Research Council
Project number:
PRG1204
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