On (m, n)-semiprime submodules
This paper aims to introduce a new class of submodules, called (m, n)-semiprime submodule, which is a generalization of semiprime submodule. Let M be a unital A-module and m, n â N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever amx â P for some a â A, x â M,...
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| Format: | Article |
| Language: | English |
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Estonian Academy Publishers
2021-08-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | https://kirj.ee/wp-content/plugins/kirj/pub/proc-3-2021-260-267_20210804190554.pdf |
| _version_ | 1828357089753300992 |
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| author | Ayten Pekin Suat Koç Emel Aslankarayiğit Uğurlu |
| author_facet | Ayten Pekin Suat Koç Emel Aslankarayiğit Uğurlu |
| author_sort | Ayten Pekin |
| collection | DOAJ |
| description | This paper aims to introduce a new class of submodules, called (m, n)-semiprime submodule, which is a generalization of semiprime submodule. Let M be a unital A-module and m, n â N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever amx â P for some a â A, x â M, then anx â P. In addition to giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules. |
| first_indexed | 2024-04-14T03:09:52Z |
| format | Article |
| id | doaj.art-da175ffcaa374306bfd797e85acad54f |
| institution | Directory Open Access Journal |
| issn | 1736-6046 1736-7530 |
| language | English |
| last_indexed | 2024-04-14T03:09:52Z |
| publishDate | 2021-08-01 |
| publisher | Estonian Academy Publishers |
| record_format | Article |
| series | Proceedings of the Estonian Academy of Sciences |
| spelling | doaj.art-da175ffcaa374306bfd797e85acad54f2022-12-22T02:15:38ZengEstonian Academy PublishersProceedings of the Estonian Academy of Sciences1736-60461736-75302021-08-0170326026710.3176/proc.2021.3.0510.3176/proc.2021.3.05On (m, n)-semiprime submodulesAyten Pekin0Suat Koç1Emel Aslankarayiğit Uğurlu2Department of Mathematics, Istanbul University, Istanbul, TurkeyDepartment of Mathematics, Marmara University, Istanbul, TurkeyDepartment of Mathematics, Marmara University, Istanbul, TurkeyThis paper aims to introduce a new class of submodules, called (m, n)-semiprime submodule, which is a generalization of semiprime submodule. Let M be a unital A-module and m, n â N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever amx â P for some a â A, x â M, then anx â P. In addition to giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules.https://kirj.ee/wp-content/plugins/kirj/pub/proc-3-2021-260-267_20210804190554.pdfsemiprime submodule(mn)-closed ideal(mn)-semiprime submodulevon neumann regular moduledescending chain condition. |
| spellingShingle | Ayten Pekin Suat Koç Emel Aslankarayiğit Uğurlu On (m, n)-semiprime submodules Proceedings of the Estonian Academy of Sciences semiprime submodule (m n)-closed ideal (m n)-semiprime submodule von neumann regular module descending chain condition. |
| title | On (m, n)-semiprime submodules |
| title_full | On (m, n)-semiprime submodules |
| title_fullStr | On (m, n)-semiprime submodules |
| title_full_unstemmed | On (m, n)-semiprime submodules |
| title_short | On (m, n)-semiprime submodules |
| title_sort | on m n semiprime submodules |
| topic | semiprime submodule (m n)-closed ideal (m n)-semiprime submodule von neumann regular module descending chain condition. |
| url | https://kirj.ee/wp-content/plugins/kirj/pub/proc-3-2021-260-267_20210804190554.pdf |
| work_keys_str_mv | AT aytenpekin onmnsemiprimesubmodules AT suatkoc onmnsemiprimesubmodules AT emelaslankarayigitugurlu onmnsemiprimesubmodules |