{"id":1248,"date":"2022-10-30T13:08:01","date_gmt":"2022-10-30T13:08:01","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1248"},"modified":"2023-12-14T16:21:18","modified_gmt":"2023-12-14T16:21:18","slug":"s-strong-mori-domain-of-a-xbx","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/s-strong-mori-domain-of-a-xbx\/","title":{"rendered":"S-strong Mori domain of A + XB[X]"},"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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S-strong Mori domain of A + XB[X]<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

Ahmed Hamed\u00a0<\/strong><\/i>
Department of Mathematics, Faculty of Sciences, Monastir, Tunisia<\/p>\n\n\n\n

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Pages 183-188 | Received 12 February 2022, Accepted 31 May 2022, Published 06 December 2022 <\/span><\/p>\n\n\n\n

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

Let A<\/span> be an integral domain and S<\/span> a multiplicative subset of A<\/span>. We say that A<\/span> is an S<\/span>-strong Mori domain (S<\/span>-SMdomain) if for each nonzero ideal I<\/span> of A<\/span> there exist an s \\in S<\/span> and a w<\/span>-finite type ideal J<\/span> of I<\/span> such that sI \\subseteq J \\subseteq I_w<\/span> ([10]). Let A \\subseteq B<\/span> be an extension of integral domains, S<\/span> an anti-Archimedean multiplicative subset of A<\/span> and X<\/span> an indeterminate over B<\/span>. In this note we give, with an additional assumption a necessary and sufficient condition for the polynomial ring A + XB[X]<\/span> to be an S<\/span>-SM-domain. <\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  S-strong Mori domains, polynomial rings. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13F05; 13E99. Secondary 13A15.<\/p>\n\n\n\n

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0102MJAGA183_188<\/a>\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles S-strong Mori domain of A + XB[X] Ahmed Hamed\u00a0 Department of Mathematics, Faculty of Sciences, Monastir, Tunisia Pages 183-188 | Received 12 February 2022, Accepted 31 May 2022, Published 06 December 2022 Abstract Let be an integral domain and a multiplicative subset of . We 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-1248","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1248","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=1248"}],"version-history":[{"count":55,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1248\/revisions"}],"predecessor-version":[{"id":2104,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1248\/revisions\/2104"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}