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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2021 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2021
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188745 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-188745 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the nilpotence of the prime radical in module categories |
| spellingShingle |
On the nilpotence of the prime radical in module categories Arellano, C. Castro, J. Ríos, J. |
| title_short |
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_sort |
on the nilpotence of the prime radical in module categories |
| author |
Arellano, C. Castro, J. Ríos, J. |
| author_facet |
Arellano, C. Castro, J. Ríos, J. |
| publishDate |
2021 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188745 |
| 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. |
| work_keys_str_mv |
AT arellanoc onthenilpotenceoftheprimeradicalinmodulecategories AT castroj onthenilpotenceoftheprimeradicalinmodulecategories AT riosj onthenilpotenceoftheprimeradicalinmodulecategories |
| first_indexed |
2025-12-07T13:13:07Z |
| last_indexed |
2025-12-07T13:13:07Z |
| _version_ |
1850855326033641472 |