{"id":2260,"date":"2024-06-29T11:05:13","date_gmt":"2024-06-29T11:05:13","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2260"},"modified":"2024-06-30T00:12:18","modified_gmt":"2024-06-30T00:12:18","slug":"absorbing-ideals-of-the-form-ix","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/absorbing-ideals-of-the-form-ix\/","title":{"rendered":"Absorbing ideals of the form $I[[X]]$"},"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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Absorbing ideals of the form I[[X]]<\/span><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Sana Hizem <\/strong><\/i>
Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia.<\/p>\n\n\n\n

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Pages 170-177 | Received 24 Augus<\/span>t 2023, Accepted 03 November 2023, Published 30 June 2024 <\/span><\/p>\n\n\n\n

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

Let R<\/span> be a commutative ring with identity and n<\/span> a positive integer. In [1], Anderson and Badawi define a proper ideal I<\/span> of a commutative ring R<\/span> to be n<\/span>-absorbing if whenever x_{1}\\cdots x_{n+1}\\in I<\/span> for x_{1},\u2026,x_{n+1}\\in R,<\/span> then there are n<\/span> of the x_{i}^{\\prime }s<\/span> whose product is in I.<\/span> In this paper we investigate the transfer of the property n<\/span>-absorbing from the ideal I<\/span> of R<\/span> to the ideal I[[X]]<\/span> of the formal power series ring R[[X]]<\/span>.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  absorbing ideals, strongly absorbing ideals, formal power series rings.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13A15; 13F25; 13F05; Secondary 13A99.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Absorbing ideals of the form Sana Hizem  Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia. Pages 170-177 | Received 24 August 2023, Accepted 03 November 2023, Published 30 June 2024 Abstract Let be a commutative ring with identity and a positive integer. In 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-2260","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2260","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=2260"}],"version-history":[{"count":5,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2260\/revisions"}],"predecessor-version":[{"id":2319,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2260\/revisions\/2319"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}