On the saturations of submodules

Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations of R-submodules of S. We use this notion of saturation to characterize star oper...

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Опубліковано в: :Algebra and Discrete Mathematics
Дата:2018
Автори: Paudel, L., Tchamna, S.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2018
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/188378
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:On the saturations of submodules / L. Paudel, S. Tchamna // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 110–123. — Бібліогр.: 8 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Paudel, L.
Tchamna, S.
author_facet Paudel, L.
Tchamna, S.
citation_txt On the saturations of submodules / L. Paudel, S. Tchamna // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 110–123. — Бібліогр.: 8 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations of R-submodules of S. We use this notion of saturation to characterize star operations ⋆ on ring extensions R ⊆ S satisfying the relation (A ∩ B)⋆ = A⋆ ∩ B⋆ whenever A and B are two R-submodules of S such that AS = BS = S.
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language English
last_indexed 2025-11-26T01:39:52Z
publishDate 2018
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Paudel, L.
Tchamna, S.
2023-02-26T12:31:31Z
2023-02-26T12:31:31Z
2018
On the saturations of submodules / L. Paudel, S. Tchamna // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 110–123. — Бібліогр.: 8 назв. — англ.
1726-3255
2010 MSC: 13A15, 13A18, 13B02.
https://nasplib.isofts.kiev.ua/handle/123456789/188378
Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations of R-submodules of S. We use this notion of saturation to characterize star operations ⋆ on ring extensions R ⊆ S satisfying the relation (A ∩ B)⋆ = A⋆ ∩ B⋆ whenever A and B are two R-submodules of S such that AS = BS = S.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
On the saturations of submodules
Article
published earlier
spellingShingle On the saturations of submodules
Paudel, L.
Tchamna, S.
title On the saturations of submodules
title_full On the saturations of submodules
title_fullStr On the saturations of submodules
title_full_unstemmed On the saturations of submodules
title_short On the saturations of submodules
title_sort on the saturations of submodules
url https://nasplib.isofts.kiev.ua/handle/123456789/188378
work_keys_str_mv AT paudell onthesaturationsofsubmodules
AT tchamnas onthesaturationsofsubmodules