{"id":2639,"date":"2025-07-26T17:12:49","date_gmt":"2025-07-26T17:12:49","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2639"},"modified":"2025-07-26T21:26:38","modified_gmt":"2025-07-26T21:26:38","slug":"weakly-s-2-prime-ideals-of-commutative-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/weakly-s-2-prime-ideals-of-commutative-rings\/","title":{"rendered":"Weakly S-2-prime ideals of commutative rings"},"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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Weakly S-2-prime ideals of commutative rings<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Sanem Yavuz\\,^1<\/span>, Bayram Ali Ersoy\\,^2<\/span>, \u00dcnsal Tekir\\,^3<\/span> and Ece Yetkin \u00c7elikel<\/strong>\\,^4<\/span><\/i>
\\,^{1,2}<\/span>Department of Mathematics, Yildiz Technical University, Istanbul, T\u00fcrkiye
\\,^{3}<\/span>Department of Mathematics, Marmara University, Istanbul, T\u00fcrkiye
\\,^{4}<\/span>Department of Software Engineering, Hasan Kalyoncu University, Gaziantep, T\u00fcrkiye<\/p>\n\n\n\n

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Pages 54-61 | Received 26 May 2024, Accepted 18 November 2024, Published 10 July 2025 <\/span><\/p>\n\n\n\n

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

The objective of this paper is to introduce and investigate the concept of weakly S<\/span>–2<\/span>-prime ideals which are extensions of weakly 2<\/span>-prime ideals in commutative rings. Let R<\/span> be a commutative ring with identity and S<\/span> be a multiplicative subset of R<\/span> with 1\\in S<\/span>. A proper ideal Q<\/span> of R<\/span> with Q\\cap S=\\emptyset<\/span> is called a weakly S<\/span>–2<\/span>-prime ideal of R<\/span> if there exists an s\\in S<\/span> such that for all \\alpha, \\ \\beta\\in R<\/span> with 0\\neq\\alpha\\beta\\in Q,<\/span> we have s\\alpha^{2}\\in Q<\/span> or s\\beta^{2}\\in Q.<\/span> Various characterizations of weakly S<\/span>–2<\/span>-prime ideals are given and the relationship between weakly S<\/span>–2<\/span>-prime ideals and other classical ideals are illustrated by a diagram. For this relationship, a myriad of supporting examples and counter examples are presented. Moreover, this class of ideals is analyzed in idealization rings and amalgamated duplication along an ideal. Besides, the rings over which every weakly S<\/span>–2<\/span>-prime ideal is S<\/span>–2<\/span>-prime ideal is examined.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  2<\/span>-prime ideals, S<\/span>–2<\/span>-prime ideals, weakly 2<\/span>-prime ideals, weakly S<\/span>–2<\/span>-prime ideals.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13A15, 13C05; Secondary 13A99.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Weakly S-2-prime ideals of commutative rings Sanem Yavuz, Bayram Ali Ersoy, \u00dcnsal Tekir and Ece Yetkin \u00c7elikel Department of Mathematics, Yildiz Technical University, Istanbul, T\u00fcrkiye Department of Mathematics, Marmara University, Istanbul, T\u00fcrkiye Department of Software Engineering, Hasan Kalyoncu University, Gaziantep, T\u00fcrkiye Pages 54-61 | Received 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-2639","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2639","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=2639"}],"version-history":[{"count":5,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2639\/revisions"}],"predecessor-version":[{"id":2700,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2639\/revisions\/2700"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}