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...
Збережено в:
| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2021
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188722 |
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dspace |
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irk-123456789-1887222023-03-13T19:15:35Z Cancellation ideals of a ring extension Tchamna, S. 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. 2021 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/188722 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Tchamna, S. |
| spellingShingle |
Tchamna, S. Cancellation ideals of a ring extension Algebra and Discrete Mathematics |
| author_facet |
Tchamna, S. |
| author_sort |
Tchamna, S. |
| title |
Cancellation ideals of a ring extension |
| title_short |
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_sort |
cancellation ideals of a ring extension |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2021 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188722 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT tchamnas cancellationidealsofaringextension |
| first_indexed |
2023-10-18T23:09:01Z |
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2023-10-18T23:09:01Z |
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