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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| Format: | Article |
| Language: | English |
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Sciendo
2024-06-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | https://doi.org/10.2478/amsil-2024-0016 |
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| _version_ | 1849310494714757120 |
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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 |