S-Semiprime Submodules and S-Reduced Modules
This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P o...
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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/10.1155/2020/8824787 |
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| author | Ayten Pekin Ünsal Tekir Özge Kılıç |
| author_facet | Ayten Pekin Ünsal Tekir Özge Kılıç |
| author_sort | Ayten Pekin |
| collection | DOAJ |
| description | This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P of M is said to be an S-semiprime submodule if there exists a fixed s∈S, and whenever rnm∈P for some r∈R,m∈M, and n∈ℕ, then srm∈P. Also, M is said to be an S-reduced module if there exists (fixed) s∈S, and whenever rnm=0 for some r∈R,m∈M, and n∈ℕ, then srm=0. In addition, to give many examples and characterizations of S-semiprime submodules and S-reduced modules, we characterize a certain class of semiprime submodules and reduced modules in terms of these concepts. |
| format | Article |
| id | doaj-art-5073ba762ac94ddca58600b4e90e98df |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5073ba762ac94ddca58600b4e90e98df2025-08-20T02:05:10ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88247878824787S-Semiprime Submodules and S-Reduced ModulesAyten Pekin0Ünsal Tekir1Özge Kılıç2Department of Mathematics, Istanbul University, Istanbul, TurkeyDepartment of Mathematics, Marmara University, Istanbul, TurkeyDepartment of Mathematics, Marmara University, Istanbul, TurkeyThis article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P of M is said to be an S-semiprime submodule if there exists a fixed s∈S, and whenever rnm∈P for some r∈R,m∈M, and n∈ℕ, then srm∈P. Also, M is said to be an S-reduced module if there exists (fixed) s∈S, and whenever rnm=0 for some r∈R,m∈M, and n∈ℕ, then srm=0. In addition, to give many examples and characterizations of S-semiprime submodules and S-reduced modules, we characterize a certain class of semiprime submodules and reduced modules in terms of these concepts.http://dx.doi.org/10.1155/2020/8824787 |
| spellingShingle | Ayten Pekin Ünsal Tekir Özge Kılıç S-Semiprime Submodules and S-Reduced Modules Journal of Mathematics |
| title | S-Semiprime Submodules and S-Reduced Modules |
| title_full | S-Semiprime Submodules and S-Reduced Modules |
| title_fullStr | S-Semiprime Submodules and S-Reduced Modules |
| title_full_unstemmed | S-Semiprime Submodules and S-Reduced Modules |
| title_short | S-Semiprime Submodules and S-Reduced Modules |
| title_sort | s semiprime submodules and s reduced modules |
| url | http://dx.doi.org/10.1155/2020/8824787 |
| work_keys_str_mv | AT aytenpekin ssemiprimesubmodulesandsreducedmodules AT unsaltekir ssemiprimesubmodulesandsreducedmodules AT ozgekılıc ssemiprimesubmodulesandsreducedmodules |