{"id":930,"date":"2022-03-29T13:14:43","date_gmt":"2022-03-29T13:14:43","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=930"},"modified":"2022-07-04T11:14:52","modified_gmt":"2022-07-04T11:14:52","slug":"formal-power-series-rings-with-one-absorbing-factorization","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/formal-power-series-rings-with-one-absorbing-factorization\/","title":{"rendered":"Formal power series rings with one absorbing factorization"},"content":{"rendered":"\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n

Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

Latest articles<\/a><\/p>\n<\/div>\n\n\n\n

\n
<\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n
\n
\n

Formal power series rings with one absorbing factorization<\/strong><\/em><\/em><\/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

<\/div>\n\n\n\n

Pages 132-138 | Received 01 December<\/span><\/span> 2021, Accepted 05 February 2022, Published 01 June<\/span><\/span><\/span><\/span> 2022 <\/span><\/p>\n\n\n\n

\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n

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

Let R<\/span> be a commutative ring with identity. A proper ideal I<\/span> of R<\/span> is said to be 1-absorbing prime ideal if whenever xyz \\in I<\/span> for some nonunit elements x,y,z\\in R,<\/span> then either xy\\in I<\/span> or z\\in I.<\/span> The ring R<\/span> is called a 1-absorbing prime factorization ring (OAF-ring) if every proper ideal has an OA-factorization. In this note, we characterize commutative rings R<\/span> (respectively, ring extensions A\\subset B<\/span>) for which the ring of formal power series R[[X]]<\/span> (respectively, the ring A+XB[X]<\/span> or A+XB[[X]]<\/span>) is an OAF-ring.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  OA-ideals, OAF-rings, formal power series rings. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13A15, 13B25, 3F25, 13F15, 13B99.<\/p>\n\n\n\n

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

<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
0101MJAGA132_138<\/a>\n

<\/p>\n<\/div>\n\n\n\n

<\/div>\n<\/div>\n\n\n\n
\n
\n
\n
Previous article <\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
View<\/strong> issue table of contents<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
Next<\/strong> article<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Moroccan Journal of Algebra and Geometry with Applications Latest articles Formal power series rings with one absorbing factorization Sana Hizem Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia Pages 132-138 | Received 01 December 2021, Accepted 05 February 2022, Published 01 June 2022 Abstract Let be a commutative ring with identity. A proper 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-930","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/930","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=930"}],"version-history":[{"count":8,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/930\/revisions"}],"predecessor-version":[{"id":1121,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/930\/revisions\/1121"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}