{"id":915,"date":"2022-03-29T12:13:09","date_gmt":"2022-03-29T12:13:09","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=915"},"modified":"2022-07-04T11:13:08","modified_gmt":"2022-07-04T11:13:08","slug":"on-two-classes-of-modules-related-to-cs-trivial-extensions","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-two-classes-of-modules-related-to-cs-trivial-extensions\/","title":{"rendered":"On two classes of modules related to CS trivial extensions"},"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 two classes of modules related to CS trivial extensions<\/strong><\/em><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

Farid Kourki & Rachid Tribak <\/strong><\/i>
Centre R\u00e9gional des M\u00e9tiers de l\u2019Education et de la Formation (CRMEF)-Tanger, Annexe de
Larache, B.P. 4063, Larache, Morocco;
Centre R\u00e9gional des M\u00e9tiers de l\u2019Education et de la Formation (CRMEF)-Tanger, Avenue My
Abdelaziz, Souani, B.P. 3117, Tangier, Morocco<\/p>\n\n\n\n

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Pages 108-121 | Received 04 November<\/span><\/span> 2021, Accepted 28 January 2022, Published 01 June<\/span><\/span> 2022 <\/span><\/p>\n\n\n\n

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

All rings considered are commutative. In this article we introduce and study two notions of modules which are stronger than CS modules, namely weakly IN modules and strongly CS modules. Our main aim is to characterize when a trivial extension A = R \\propto M<\/span> (of a ring R<\/span> by an R<\/span>-module M<\/span>) is a CS ring.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  CS-ring, strongly CS module (ring), trivial extension, weakly IN module (ring). <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 16D10, 16D70; Secondary 16D80.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On two classes of modules related to CS trivial extensions Farid Kourki & Rachid Tribak Centre R\u00e9gional des M\u00e9tiers de l\u2019Education et de la Formation (CRMEF)-Tanger, Annexe de Larache, B.P. 4063, Larache, Morocco; Centre R\u00e9gional des M\u00e9tiers de l\u2019Education et de la Formation (CRMEF)-Tanger, Avenue 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-915","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/915","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=915"}],"version-history":[{"count":8,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/915\/revisions"}],"predecessor-version":[{"id":1119,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/915\/revisions\/1119"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}