Cancellation ideals of a ring extension
We study properties of cancellation ideals of ring extensions. Let R ⊆ S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R ⊆ S if whenever IB = IC for two S-regular (finitely generated) R-submodules B and C of S, then B = C. We show...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188722 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Cancellation ideals of a ring extension / S. Tchamna // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 1. — С. 138–146. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862597265572495360 |
|---|---|
| author | Tchamna, S. |
| author_facet | Tchamna, S. |
| citation_txt | Cancellation ideals of a ring extension / S. Tchamna // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 1. — С. 138–146. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We study properties of cancellation ideals of ring extensions. Let R ⊆ S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R ⊆ S if whenever IB = IC for two S-regular (finitely generated) R-submodules B and C of S, then B = C. We show that a finitely generated ideal I is a cancellation ideal of the ring extension R ⊆ S if and only if I is S-invertible.
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| first_indexed | 2025-11-27T17:25:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188722 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-27T17:25:12Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Tchamna, S. 2023-03-12T18:34:08Z 2023-03-12T18:34:08Z 2021 Cancellation ideals of a ring extension / S. Tchamna // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 1. — С. 138–146. — Бібліогр.: 7 назв. — англ. 1726-3255 DOI:10.12958/adm1424 2020 MSC: 13A15, 13A18, 13B02 https://nasplib.isofts.kiev.ua/handle/123456789/188722 We study properties of cancellation ideals of ring extensions. Let R ⊆ S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R ⊆ S if whenever IB = IC for two S-regular (finitely generated) R-submodules B and C of S, then B = C. We show that a finitely generated ideal I is a cancellation ideal of the ring extension R ⊆ S if and only if I is S-invertible. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Cancellation ideals of a ring extension Article published earlier |
| spellingShingle | Cancellation ideals of a ring extension Tchamna, S. |
| title | Cancellation ideals of a ring extension |
| title_full | Cancellation ideals of a ring extension |
| title_fullStr | Cancellation ideals of a ring extension |
| title_full_unstemmed | Cancellation ideals of a ring extension |
| title_short | Cancellation ideals of a ring extension |
| title_sort | cancellation ideals of a ring extension |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188722 |
| work_keys_str_mv | AT tchamnas cancellationidealsofaringextension |