Generalizations of prime submodules over non-commutative rings
Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ∅-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the...
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University of Mohaghegh Ardabili
2023-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_2528_bd5804334486f1a38b22b02c15efca60.pdf |
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| author | Emel Aslankarayigit Ugurlu |
| author_facet | Emel Aslankarayigit Ugurlu |
| author_sort | Emel Aslankarayigit Ugurlu |
| collection | DOAJ |
| description | Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ∅-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and Ø : S(M) ! S(M) [ f;g is a function. For every Y 2 S(M) and ideal I of R; a proper submodule X of M is called Ø-prime, if YI ⊆ X and YI ⊄ Ø(X); then Y ⊆ X or I ⊆ (X :R M): Then we examine the properties of Ø-prime submodules and characterize it when M is a multiplication module. |
| format | Article |
| id | doaj-art-8dd55882c8244b0ab37e5c3d6817ee7f |
| institution | DOAJ |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-8dd55882c8244b0ab37e5c3d6817ee7f2025-08-20T02:40:20ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662023-06-01111658310.22098/jhs.2023.25282528Generalizations of prime submodules over non-commutative ringsEmel Aslankarayigit Ugurlu0Department of Mathematics, Marmara University, P.O.Box 34722, Istanbul, TurkeyThroughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ∅-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and Ø : S(M) ! S(M) [ f;g is a function. For every Y 2 S(M) and ideal I of R; a proper submodule X of M is called Ø-prime, if YI ⊆ X and YI ⊄ Ø(X); then Y ⊆ X or I ⊆ (X :R M): Then we examine the properties of Ø-prime submodules and characterize it when M is a multiplication module.https://jhs.uma.ac.ir/article_2528_bd5804334486f1a38b22b02c15efca60.pdf$\phi-$prime submodulenon-commutative ringmultiplication module |
| spellingShingle | Emel Aslankarayigit Ugurlu Generalizations of prime submodules over non-commutative rings Journal of Hyperstructures $\phi-$prime submodule non-commutative ring multiplication module |
| title | Generalizations of prime submodules over non-commutative rings |
| title_full | Generalizations of prime submodules over non-commutative rings |
| title_fullStr | Generalizations of prime submodules over non-commutative rings |
| title_full_unstemmed | Generalizations of prime submodules over non-commutative rings |
| title_short | Generalizations of prime submodules over non-commutative rings |
| title_sort | generalizations of prime submodules over non commutative rings |
| topic | $\phi-$prime submodule non-commutative ring multiplication module |
| url | https://jhs.uma.ac.ir/article_2528_bd5804334486f1a38b22b02c15efca60.pdf |
| work_keys_str_mv | AT emelaslankarayigitugurlu generalizationsofprimesubmodulesovernoncommutativerings |