{"id":895,"date":"2022-03-27T17:14:31","date_gmt":"2022-03-27T17:14:31","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=895"},"modified":"2022-07-04T11:11:45","modified_gmt":"2022-07-04T11:11:45","slug":"rings-whose-cyclics-are-du-modules","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/rings-whose-cyclics-are-du-modules\/","title":{"rendered":"Rings whose cyclics are DU-modules"},"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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Rings whose cyclics are DU-modules<\/strong><\/em><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

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Yasser Ibrahim , Tamer Ko\u015fan & Mohamed Yousif <\/strong><\/i>
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt and,
Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia;
Department of Mathematics, Gazi University, Ankara, Turkey;
Department of Mathematics, The Ohio State University, Lima, Ohio 45804, USA.<\/p>\n\n\n\n

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Pages 86-97 | Received 10 June 2021, Accepted 03 August 2021, Published 01 June<\/span> 2022 <\/span><\/p>\n\n\n\n

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

A right R<\/span>-module M<\/span> is called a D 4<\/span>-Module if for any two direct summands A<\/span> and B<\/span> of M<\/span> with M =A +B<\/span> and M\/A \\cong M\/B<\/span>, we have A \\cap B \\subseteq ^{ \\oplus }M<\/span>. The module M<\/span> is called a Dual-Utumi-Module (D U<\/span>-module) if M<\/span> is a D 4<\/span>-module and for any two proper submodules A<\/span> and B<\/span> of M<\/span> with M\/A \\cong M\/B<\/span> and A +B =M<\/span>, both A<\/span> and B<\/span> lie over direct summands of M<\/span>. The notion of D U<\/span>-modules is a simultaneous and strict generalization of both the quasi-discrete as well as the dual-square-free modules. In this paper,we study the modules whose factors are D U<\/span>-modules (D 4<\/span>-modules), extending some of the known results on quasi-discrete modules and obtaining new ones. <\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Projective, quasi-projective, quasi-discrete, Utumi, Dual-Utumi and dual-square-free modules. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 16D40, 16D50, 16D60; Secondary 16L30, 16L60, 16P20, 16P40, 16P60.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Rings whose cyclics are DU-modules Yasser Ibrahim , Tamer Ko\u015fan & Mohamed Yousif Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt and, Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia;Department of Mathematics, Gazi University, Ankara, Turkey; Department of Mathematics, The Ohio 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-895","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/895","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=895"}],"version-history":[{"count":17,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/895\/revisions"}],"predecessor-version":[{"id":1117,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/895\/revisions\/1117"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}