A Note on Abelian Groups Supporting Unital Rings

Non-nil abelian groups are classified on which every ring, different from the zero-ring, is unital. It is shown that the assumption on the associativity of the considered rings does not influence the obtained classification. A significant mistake made by other authors studied this topic is corrected...

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Main Author: Woronowicz Mateusz
Format: Article
Language:English
Published: Sciendo 2024-06-01
Series:Annales Mathematicae Silesianae
Subjects:
Online Access:https://doi.org/10.2478/amsil-2024-0016
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author Woronowicz Mateusz
author_facet Woronowicz Mateusz
author_sort Woronowicz Mateusz
collection DOAJ
description Non-nil abelian groups are classified on which every ring, different from the zero-ring, is unital. It is shown that the assumption on the associativity of the considered rings does not influence the obtained classification. A significant mistake made by other authors studied this topic is corrected.
format Article
id doaj-art-30f27d47fc46411faf3ff0e2ac848aa1
institution Kabale University
issn 2391-4238
language English
publishDate 2024-06-01
publisher Sciendo
record_format Article
series Annales Mathematicae Silesianae
spelling doaj-art-30f27d47fc46411faf3ff0e2ac848aa12025-08-20T03:53:42ZengSciendoAnnales Mathematicae Silesianae2391-42382024-06-0139117017610.2478/amsil-2024-0016A Note on Abelian Groups Supporting Unital RingsWoronowicz Mateusz0Faculty of Mathematics, University of Bialystok, 1M, Ciolkowskiego Street 15-245Bialystok, PolandNon-nil abelian groups are classified on which every ring, different from the zero-ring, is unital. It is shown that the assumption on the associativity of the considered rings does not influence the obtained classification. A significant mistake made by other authors studied this topic is corrected.https://doi.org/10.2478/amsil-2024-001620k9916b99abelian groupsadditive groups of ringsunital rings
spellingShingle Woronowicz Mateusz
A Note on Abelian Groups Supporting Unital Rings
Annales Mathematicae Silesianae
20k99
16b99
abelian groups
additive groups of rings
unital rings
title A Note on Abelian Groups Supporting Unital Rings
title_full A Note on Abelian Groups Supporting Unital Rings
title_fullStr A Note on Abelian Groups Supporting Unital Rings
title_full_unstemmed A Note on Abelian Groups Supporting Unital Rings
title_short A Note on Abelian Groups Supporting Unital Rings
title_sort note on abelian groups supporting unital rings
topic 20k99
16b99
abelian groups
additive groups of rings
unital rings
url https://doi.org/10.2478/amsil-2024-0016
work_keys_str_mv AT woronowiczmateusz anoteonabeliangroupssupportingunitalrings
AT woronowiczmateusz noteonabeliangroupssupportingunitalrings