Uniformly Primal Submodule over Noncommutative Ring
Let R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N, if there exists an element s∈M−N with sRB⊆N.The set adjN=r∈R|mRr⊆N for some m∈M is uniformly not...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/1593253 |
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| author | Lamis J. M. Abulebda |
| author_facet | Lamis J. M. Abulebda |
| author_sort | Lamis J. M. Abulebda |
| collection | DOAJ |
| description | Let R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N, if there exists an element s∈M−N with sRB⊆N.The set adjN=r∈R|mRr⊆N for some m∈M is uniformly not prime to N.This paper is concerned with the properties of uniformly primal submodules. Also, we generalize the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules. |
| format | Article |
| id | doaj-art-94c8da7440a04861ae57bcc15617799e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-94c8da7440a04861ae57bcc15617799e2025-02-03T06:45:53ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/15932531593253Uniformly Primal Submodule over Noncommutative RingLamis J. M. Abulebda0Department of Mathematics, College of Arts and Sciences, University of Balamand Dubai, Dubai, UAELet R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N, if there exists an element s∈M−N with sRB⊆N.The set adjN=r∈R|mRr⊆N for some m∈M is uniformly not prime to N.This paper is concerned with the properties of uniformly primal submodules. Also, we generalize the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules.http://dx.doi.org/10.1155/2020/1593253 |
| spellingShingle | Lamis J. M. Abulebda Uniformly Primal Submodule over Noncommutative Ring Journal of Mathematics |
| title | Uniformly Primal Submodule over Noncommutative Ring |
| title_full | Uniformly Primal Submodule over Noncommutative Ring |
| title_fullStr | Uniformly Primal Submodule over Noncommutative Ring |
| title_full_unstemmed | Uniformly Primal Submodule over Noncommutative Ring |
| title_short | Uniformly Primal Submodule over Noncommutative Ring |
| title_sort | uniformly primal submodule over noncommutative ring |
| url | http://dx.doi.org/10.1155/2020/1593253 |
| work_keys_str_mv | AT lamisjmabulebda uniformlyprimalsubmoduleovernoncommutativering |