{"id":2605,"date":"2025-07-26T14:30:04","date_gmt":"2025-07-26T14:30:04","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2605"},"modified":"2025-07-26T21:23:36","modified_gmt":"2025-07-26T21:23:36","slug":"on-graded-almost-bezout-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-graded-almost-bezout-rings\/","title":{"rendered":"On graded almost-B\u00e9zout 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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On graded almost-B\u00e9zout rings<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Fatima-Zahra Guissi\\,^1<\/span> and Najib Mahdou<\/strong>\\,^2<\/span><\/i>
\\,^{1,2}<\/span>Department of Mathematics, Faculty of Science and Technology, Fez, Morocco<\/p>\n\n\n\n

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Pages 1-10 | Received 14 May 2024, Accepted 28 August 2024, Published 10 July 2025 <\/span><\/p>\n\n\n\n

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

Let R=\\bigoplus_{\\alpha\\in\\Gamma}R_{\\alpha}<\/span> be a commutative ring graded by an arbitrary abelian group \\Gamma<\/span>. We say that R<\/span> is graded almost-B\u00e9zout ring if for each a,b\\in h(R),<\/span> there exists n\\geq 1<\/span> and x\\in h(R)<\/span> such that (a^{n},b^{n})=(x)<\/span>. In this paper, we investigate the transfer of this property in different graded commutative ring extensions, namely, in graded trivial ring extensions (A \\ltimes E<\/span>) and graded amalgamated algebras along an ideal (A \\bowtie^f J<\/span>). Our aim is to provide examples of new classes of \\Gamma<\/span>-graded rings satisfying the above mentioned property.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Graded almost B\u00e9zout ring, graded amalgamation of ring, gr-B\u00e9zout ring, graded trivial ring extension.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13A02, 13C13.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On graded almost-B\u00e9zout rings Fatima-Zahra Guissi and Najib Mahdou Department of Mathematics, Faculty of Science and Technology, Fez, Morocco Pages 1-10 | Received 14 May 2024, Accepted 28 August 2024, Published 10 July 2025 Abstract Let be a commutative ring graded by an arbitrary abelian 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-2605","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2605","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=2605"}],"version-history":[{"count":8,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2605\/revisions"}],"predecessor-version":[{"id":2695,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2605\/revisions\/2695"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}