On Strongly 𝝅-regular Modules
In this article, we introduce the notion of strongly π-regular module which is a generalization of von Neumann regular module in the sense [13]. Let A be a commutative ring with 1≠0 and X a multiplication A-module. X is called a strongly π-regular module if for each x∈X, 〖(Ax)〗^m=cX=c^2 X for some c...
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Sakarya University
2020-08-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1210245 |
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| author | Suat Koç |
| author_facet | Suat Koç |
| author_sort | Suat Koç |
| collection | DOAJ |
| description | In this article, we introduce the notion of strongly π-regular module which is a generalization of von Neumann regular module in the sense [13]. Let A be a commutative ring with 1≠0 and X a multiplication A-module. X is called a strongly π-regular module if for each x∈X, 〖(Ax)〗^m=cX=c^2 X for some c∈A and m∈N. In addition to give many properties and examples of strongly π-regular modules, we also characterize certain class of modules such as von Neumann regular modules and second modules in terms of this new class of modules. Also, we determine when the localization of any family of submodules at a prime ideal commutes with the intersection of this family. |
| format | Article |
| id | doaj-art-93b8426f1e594cb5a2aaebe87a7a2479 |
| institution | OA Journals |
| issn | 2147-835X |
| language | English |
| publishDate | 2020-08-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-93b8426f1e594cb5a2aaebe87a7a24792025-08-20T02:31:51ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2020-08-0124467568410.16984/saufenbilder.69636628On Strongly 𝝅-regular ModulesSuat Koç0https://orcid.org/0000-0003-1622-786XMarmara UniversityIn this article, we introduce the notion of strongly π-regular module which is a generalization of von Neumann regular module in the sense [13]. Let A be a commutative ring with 1≠0 and X a multiplication A-module. X is called a strongly π-regular module if for each x∈X, 〖(Ax)〗^m=cX=c^2 X for some c∈A and m∈N. In addition to give many properties and examples of strongly π-regular modules, we also characterize certain class of modules such as von Neumann regular modules and second modules in terms of this new class of modules. Also, we determine when the localization of any family of submodules at a prime ideal commutes with the intersection of this family.https://dergipark.org.tr/tr/download/article-file/1210245von neumann regular module(m n)-closed idealstrongly π-regular modulekrull dimension(∗)-propertylocalization |
| spellingShingle | Suat Koç On Strongly 𝝅-regular Modules Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi von neumann regular module (m n)-closed ideal strongly π-regular module krull dimension (∗)-property localization |
| title | On Strongly 𝝅-regular Modules |
| title_full | On Strongly 𝝅-regular Modules |
| title_fullStr | On Strongly 𝝅-regular Modules |
| title_full_unstemmed | On Strongly 𝝅-regular Modules |
| title_short | On Strongly 𝝅-regular Modules |
| title_sort | on strongly 𝝅 regular modules |
| topic | von neumann regular module (m n)-closed ideal strongly π-regular module krull dimension (∗)-property localization |
| url | https://dergipark.org.tr/tr/download/article-file/1210245 |
| work_keys_str_mv | AT suatkoc onstronglyπregularmodules |