{"id":2265,"date":"2024-06-29T11:16:47","date_gmt":"2024-06-29T11:16:47","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2265"},"modified":"2024-06-30T00:12:41","modified_gmt":"2024-06-30T00:12:41","slug":"on-phi-prufer-and-phi-bezout-rings-in-amalgamation-algebra-along-an-ideal","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-phi-prufer-and-phi-bezout-rings-in-amalgamation-algebra-along-an-ideal\/","title":{"rendered":"On $\\phi$-Pr\u00fcfer and $\\phi$-B\u00e9zout rings in amalgamation algebra along an ideal"},"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 \\phi<\/span><\/strong>-Pr\u00fcfer and \\phi<\/span><\/strong>-B\u00e9zout rings in amalgamation algebra along an ideal<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Younes El Haddaoui <\/strong><\/i>
Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia.<\/p>\n\n\n\n

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Pages 178-186 | Received 08 September<\/span> 2023, Accepted 13 December 2023, Published 30 June 2024 <\/span><\/p>\n\n\n\n

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

In this paper, all rings considered are assumed commutative with nonzero identity. A ring R<\/span> is said to be \\phi<\/span>-ring if its Nilradical is divided and prime ideal. The authors of [2] introduced and studied two new generalizations of Pr\u00fcfer domains and B\u00e9zout domains respectively, a ring R<\/span> is said to be \\phi<\/span>-Pr\u00fcfer ring (resp., \\phi<\/span>-B\u00e9zout ring) provided that R\/Nil(R)<\/span> is a Pr\u00fcfer domain (resp., a B\u00e9zout domain). In this work, we study the notions of \\phi<\/span>-Pr\u00fcfer rings and \\phi<\/span>-B\u00e9zout ring in different contexts of commutative rings such us trivial ring extensions and amalgamations of algebras along ideals. Our aim is to generate new families of \\phi<\/span>-Pr\u00fcfer rings and \\phi<\/span>-B\u00e9zout rings 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

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Keywords<\/strong>:<\/span>  \\phi<\/span>-Pr\u00fcfer rings, \\phi<\/span>-B\u00e9zout rings, nonnil coherent rings, \\phi<\/span>-coherent rings.<\/p>\n\n\n\n

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

Downloads:<\/strong> Full-text PDF<\/a><\/p>\n<\/div>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On -Pr\u00fcfer and -B\u00e9zout rings in amalgamation algebra along an ideal Younes El Haddaoui  Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia. Pages 178-186 | Received 08 September 2023, Accepted 13 December 2023, Published 30 June 2024 Abstract In this paper, all rings 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-2265","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2265","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=2265"}],"version-history":[{"count":6,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2265\/revisions"}],"predecessor-version":[{"id":2320,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2265\/revisions\/2320"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}