{"id":1767,"date":"2023-06-14T17:33:17","date_gmt":"2023-06-14T17:33:17","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1767"},"modified":"2023-10-12T22:08:39","modified_gmt":"2023-10-12T22:08:39","slug":"note-on-un-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/note-on-un-rings\/","title":{"rendered":"Note on UN-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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Note on UN-rings
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Abdeslam Mimouni <\/strong><\/i>
Department of Mathematics, KFUPM, Dhahran 31261, KSA<\/p>\n\n\n\n

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Pages 1<\/span>43-153 | Received 10 February 2023, Accepted 07 April 2023, Published 16 June 2023 <\/span><\/p>\n\n\n\n

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

Let R<\/span> be an associative ring with identity. Then R<\/span> is said to be a UN<\/span>-ring if every nonunit element of R<\/span> can be written as a product of a unit and nilpotent elements. If in every UN<\/span>-decomposition, the unit and nilpotent commute, the ring R<\/span> is said to be a strongly UN<\/span>-ring. In this paper, we study the notions of UN<\/span>-rings in different contexts of commutative rings such us pullbacks, trivial ring extensions and amalgamations of algebras along ideals. Our aim is to generate new families of UN<\/span>-rings. Namely, constructing UN<\/span>-rings issued from pullbacks where the starting rings are not necessarily UN<\/span>-ring and also to enrich the literature with such a rings. Examples illustrating the aims and scopes of our results are given.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  UN<\/span>-ring, strongly UN<\/span>-ring, pullbacks, trivial ring extension, amalgamation. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13A15, 13A18, 13F05, 13G05, 13C20.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Note on UN-rings Abdeslam Mimouni  Department of Mathematics, KFUPM, Dhahran 31261, KSA Pages 143-153 | Received 10 February 2023, Accepted 07 April 2023, Published 16 June 2023 Abstract Let be an associative ring with identity. Then is said to be a -ring if every nonunit 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-1767","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1767","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=1767"}],"version-history":[{"count":5,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1767\/revisions"}],"predecessor-version":[{"id":1943,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1767\/revisions\/1943"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1767"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}