{"id":2228,"date":"2024-06-28T14:16:30","date_gmt":"2024-06-28T14:16:30","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2228"},"modified":"2024-06-30T00:10:05","modified_gmt":"2024-06-30T00:10:05","slug":"on-semi-radical-ideals-of-noncommutative-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-semi-radical-ideals-of-noncommutative-rings\/","title":{"rendered":"On semi radical ideals of noncommutative rings"},"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 semi radical ideals of noncommutative rings<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Nico Groenewald <\/strong><\/i>
Department of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa.<\/p>\n\n\n\n

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Pages 23-35 | Received 01 July 2023, Accepted 21 September 2023, Published 30 June 2024<\/span> <\/span><\/p>\n\n\n\n

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

Since the introduction of n<\/span>-ideals and J<\/span>-ideals in commutative rings many different aspects of these ideals have been investigated. As a generalization the notion of weakly n<\/span>-ideals and weakly J<\/span>-ideals was introduced and studied. Recently it was proved that many of the results are also true for noncommutative rings as a special case of a more general situation. In a recent paper Khashan et. al introduced the notion of semi n<\/span>-ideals as a generalization of n<\/span>-ideals where n<\/span> is the prime radical and studied this generalization. In this note we show that these results are special cases of a more general situation. If \\rho<\/span> is a special radical and R<\/span> a noncommutative ring then the ideal I<\/span> of R<\/span> is a semi \\rho<\/span>-ideal if aRa \\subseteq I<\/span>, then a \\in \\rho (R)<\/span> or a \\in I<\/span>. This covers a wide spectrum of semi ideals and if \\rho<\/span> is the prime radical we have the notion of semi n<\/span>-ideals for noncommutative rings. In this note we prove that most of the results for the semi n<\/span>-ideals are satisfied for noncommutative rings as a special case.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Special radical, semi n<\/span>-ideal, semi \\rho<\/span>-ideal, semi \\rho<\/span>-submodule.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 16N20, 16N40, 16N80, 16L30.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On semi radical ideals of noncommutative rings Nico Groenewald  Department of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa. Pages 23-35 | Received 01 July 2023, Accepted 21 September 2023, Published 30 June 2024 Abstract Since the introduction of -ideals and -ideals in commutative 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-2228","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2228","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=2228"}],"version-history":[{"count":4,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2228\/revisions"}],"predecessor-version":[{"id":2314,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2228\/revisions\/2314"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}