{"id":2384,"date":"2024-11-02T20:27:07","date_gmt":"2024-11-02T20:27:07","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2384"},"modified":"2026-01-26T08:41:47","modified_gmt":"2026-01-26T08:41:47","slug":"on-phi-1-absorbing-primary-submodules","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-phi-1-absorbing-primary-submodules\/","title":{"rendered":"On $\\phi$-1-absorbing primary submodules"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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On \\phi<\/span>-1-absorbing primary submodules<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

\u00dcnsal Tekir\\,^1<\/span> <\/strong><\/i>, Eda Y\u0131ld\u0131z\\,^2<\/span>, Suat Ko\u00e7\\,^3<\/span> and Ece Yetkin \u00c7elikel\\,^4<\/span>
\\,^1<\/span>Department of Mathematics, Marmara University, Istanbul, Turkey.
\\,^2<\/span>Department of Mathematics, Yildiz Technical University, Istanbul, Turkey.
\\,^3<\/span>Deparment of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey.
\\,^4<\/span>Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Turkey.<\/p>\n\n\n\n

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Pages 232\u2013242 | Received 20 November 2023, Accepted 27 January 2024, Published 08 November 2024 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

In this article, we introduce \\phi<\/span>-1-absorbing primary submodules of modules over commutative rings. Let R\\ <\/span>be a commutative ring with a nonzero identity and M\\ <\/span>be a nonzero unital module. \\phi:\\mathcal{S}(M)\\rightarrow \\mathcal{S}(M)\\cup{\\emptyset}<\/span> be a function where \\mathcal{S}(M)<\/span> is the set of all submodules of M<\/span>. A proper submodule N\\ <\/span>of M\\ <\/span>is said to be a \\phi<\/span>-1-absorbing primary submodule if whenever abm\\in N-\\phi(N)<\/span> for some nonunit elements a,b\\in R\\ <\/span>and m\\in M,\\ <\/span>then ab\\in(N:_{R}M)\\ <\/span>or m\\in M<\/span>–rad(N),\\ <\/span>where M<\/span>–rad(N)<\/span> is the prime radical of N.\\ <\/span>Many properties and characterizations of \\phi<\/span>-1-absorbing primary submodules are given. We also give the relations between \\phi<\/span>-1-absorbing primary submodules and other classical submodules such as \\phi<\/span>-prime, \\phi<\/span>-primary, \\phi <\/span>-2-absorbing primary submodules.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  \\phi<\/span>-prime submodule, 1-absorbing primary submodule, (weakly) pseudo primary submodule, \\phi<\/span>-1-absorbing primary submodule.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13A15; Secondary 16D60.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On -1-absorbing primary submodules \u00dcnsal Tekir , Eda Y\u0131ld\u0131z, Suat Ko\u00e7 and Ece Yetkin \u00c7elikel Department of Mathematics, Marmara University, Istanbul, Turkey. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey. Deparment of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey. Department of Basic Sciences, Faculty of Engineering, Hasan Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2384","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2384","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2384"}],"version-history":[{"count":7,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2384\/revisions"}],"predecessor-version":[{"id":2506,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2384\/revisions\/2506"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2384"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}