{"id":2402,"date":"2024-11-02T21:37:11","date_gmt":"2024-11-02T21:37:11","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2402"},"modified":"2024-11-08T08:15:39","modified_gmt":"2024-11-08T08:15:39","slug":"generalized-s-prime-ideals-of-commutative-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/generalized-s-prime-ideals-of-commutative-rings\/","title":{"rendered":"Generalized S-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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Generalized S-prime ideals of commutative rings<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Ahmed Hamed <\/strong><\/i>
Department of Mathematics, Faculty of Sciences, University of Monastir, Monastir, Tunisia<\/p>\n\n\n\n

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Pages 279\u2013287 | Received 09 November 2023, Accepted 22 February 2024, Published 08 November 2024 <\/span><\/p>\n\n\n\n

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

If 3 \\leq n \\leq \\infty<\/span>, Let R<\/span> be a commutative ring with identity and S<\/span> a multiplicative subset of R.<\/span> The purpose of this paper is to introduce the concept of generalized S<\/span>-prime ideals as a new generalization of prime ideals. An ideal P<\/span> of R<\/span> disjoint with S<\/span> is called a generalized S<\/span>-prime ideal if for all \\alpha, \\beta\\in R<\/span> there exists an s\\in S<\/span> such that \\alpha\\beta\\in P<\/span> implies s\\alpha\\in P<\/span> or s\\beta\\in P.<\/span> Several properties, characterizations and examples concerning generalized S<\/span>-prime ideals are presented. We give a relationship between generalized S<\/span>-prime ideals of a ring R<\/span> and those of the idealization ring R(+)M.<\/span> Also, we show that each ideal of R<\/span> disjoint with S<\/span> is contained in a minimal generalized S<\/span>-prime ideal of R.<\/span> This extends classical well-known result on minimal prime ideals.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Generalized S<\/span>-prime ideal, S<\/span>-prime ideal.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13A15.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Generalized S-prime ideals of commutative rings Ahmed Hamed Department of Mathematics, Faculty of Sciences, University of Monastir, Monastir, Tunisia Pages 279\u2013287 | Received 09 November 2023, Accepted 22 February 2024, Published 08 November 2024 Abstract If , Let be a commutative ring with identity and 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-2402","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2402","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=2402"}],"version-history":[{"count":7,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2402\/revisions"}],"predecessor-version":[{"id":2510,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2402\/revisions\/2510"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}