On the nilpotence of the prime radical in module categories
For M ∈ R-Mod and τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ (M) = Nτ as the intersection of all τ-pure prime submodules of M. We give necessary and sufficient conditi...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2021 |
| Автори: | , , |
| 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/123456789/188745 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the nilpotence of the prime radical in module categories / C. Arellano, J. Castro, J. Ríos // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 161-184. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862617848618156032 |
|---|---|
| author | Arellano, C. Castro, J. Ríos, J. |
| author_facet | Arellano, C. Castro, J. Ríos, J. |
| citation_txt | On the nilpotence of the prime radical in module categories / C. Arellano, J. Castro, J. Ríos // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 161-184. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | For M ∈ R-Mod and τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ (M) = Nτ as the intersection of all τ-pure prime submodules of M. We give necessary and sufficient conditions for the τ -nilpotence of Nτ(M). We prove that if M is a finitely generated R-module, progenerator in σ[M] and χ ≠ τ is FIS-invariant torsion theory such that M has τ -Krull dimension, then Nτ is τ -nilpotent.
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| first_indexed | 2025-12-07T13:13:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188745 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:13:07Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Arellano, C. Castro, J. Ríos, J. 2023-03-14T16:40:18Z 2023-03-14T16:40:18Z 2021 On the nilpotence of the prime radical in module categories / C. Arellano, J. Castro, J. Ríos // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 161-184. — Бібліогр.: 18 назв. — англ. 1726-3255 DOI:10.12958/adm1634 2020 MSC: 06F25, 16S90, 16D50, 16P50, 16P70 https://nasplib.isofts.kiev.ua/handle/123456789/188745 For M ∈ R-Mod and τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ (M) = Nτ as the intersection of all τ-pure prime submodules of M. We give necessary and sufficient conditions for the τ -nilpotence of Nτ(M). We prove that if M is a finitely generated R-module, progenerator in σ[M] and χ ≠ τ is FIS-invariant torsion theory such that M has τ -Krull dimension, then Nτ is τ -nilpotent. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the nilpotence of the prime radical in module categories Article published earlier |
| spellingShingle | On the nilpotence of the prime radical in module categories Arellano, C. Castro, J. Ríos, J. |
| title | On the nilpotence of the prime radical in module categories |
| title_full | On the nilpotence of the prime radical in module categories |
| title_fullStr | On the nilpotence of the prime radical in module categories |
| title_full_unstemmed | On the nilpotence of the prime radical in module categories |
| title_short | On the nilpotence of the prime radical in module categories |
| title_sort | on the nilpotence of the prime radical in module categories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188745 |
| work_keys_str_mv | AT arellanoc onthenilpotenceoftheprimeradicalinmodulecategories AT castroj onthenilpotenceoftheprimeradicalinmodulecategories AT riosj onthenilpotenceoftheprimeradicalinmodulecategories |