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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Published in:Algebra and Discrete Mathematics
Date:2021
Main Author: Tchamna, S.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2021
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/188722
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
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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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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