{"id":2032,"date":"2023-12-08T20:15:40","date_gmt":"2023-12-08T20:15:40","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2032"},"modified":"2023-12-11T13:40:15","modified_gmt":"2023-12-11T13:40:15","slug":"on-weakly-prime-ideals-and-weak-krull-dimension","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-weakly-prime-ideals-and-weak-krull-dimension\/","title":{"rendered":"On weakly prime ideals and weak Krull dimension"},"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

On weakly prime ideals and weak Krull dimension<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Najib Mahdou\\,^1 <\/span>, Abdeslam Mimouni\\,^2 <\/span> and Youssef Zahir<\/strong>\\,^3 <\/span> <\/i>
\\,^1 <\/span>Laboratory of Algebra, Functional Analysis and Applications,Department of Mathematics, Faculty
of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco.
\\,^2 <\/span> Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, P. O. Box 278, Dhahran 31261, Saudi Arabia.
\\,^3 <\/span> Laboratory: Mathematics, Computing and Applications Information Security (LabMiA-SI),
Department of Mathematics, Faculty of Sciences of Rabat, B.P. 1014, Mohammed V University in Rabat, Morocco.<\/p>\n\n\n\n

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

Pages 307\u2013314 | <\/font> Received 21 April 2023, Accepted<\/span><\/span> 14 September 2023<\/span><\/span>, Published 11 December 2023 <\/span> <\/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 and let P<\/span> be a proper ideal of R<\/span>. The notion of weakly prime (resp., weakly semiprime) ideals are introduced by Anderson-Smith (resp., by Badawi), and considered a generalization of prime (resp., semiprime) ideals. An ideal P<\/span> is called weakly prime (resp., weakly semiprime) if 0 \\neq ab \\in P<\/span> implies a \\in P<\/span> or b \\in P<\/span> (resp., 0 \\neq a^2 \\in P<\/span> implies a \\in P<\/span>). The aim of this paper is to describe the weakly prime and weakly semiprime ideals in trivial ring extensions. Also, we introduce and study the weak Krull dimension of ring.<\/p>\n\n\n\n

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

Keywords<\/strong>:<\/span>  Weakly prime, weak Krull dimension, trivial ring extension, decomposable ring. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13F05, 13A15, 13E05, 13F20, 13C10, 13C11, 13F30, 13D05, 16D40, 16E10, 16E60.<\/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
MJAGA_Vol2_Issue2-307-314<\/a>\n

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

<\/div>\n<\/div>\n\n\n\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 On weakly prime ideals and weak Krull dimension Najib Mahdou, Abdeslam Mimouni and Youssef Zahir Laboratory of Algebra, Functional Analysis and Applications,Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco. Department of Mathematics and Statistics, King 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-2032","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2032","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=2032"}],"version-history":[{"count":9,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2032\/revisions"}],"predecessor-version":[{"id":2089,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2032\/revisions\/2089"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}