{"id":2634,"date":"2025-07-26T16:44:36","date_gmt":"2025-07-26T16:44:36","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2634"},"modified":"2025-07-26T21:25:20","modified_gmt":"2025-07-26T21:25:20","slug":"finite-direct-projective-covers-and-envelopes","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/finite-direct-projective-covers-and-envelopes\/","title":{"rendered":"Finite direct projective Covers and Envelopes"},"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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Finite direct projective Covers and Envelopes<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Sonal Gupta\\,^1<\/span>, Manoj Kumar Patel<\/strong>\\,^2<\/span><\/i> and Ashok Ji Gupta\\,^3<\/span>
\\,^{1,3}<\/span>Department of Mathematical Sciences, IIT(BHU), Varanasi, 221005, India
\\,^{2}<\/span>Department of Mathematics, National Institute of Technology Nagaland, Dimapur, 797103, India<\/p>\n\n\n\n

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Pages 46-53 | Received 02 June 2024, Accepted 17 November 2024, Published 10 July 2025 <\/span><\/p>\n\n\n\n

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

In this paper, we explore the concept of finite direct projective covers and envelopes. We identify the conditions under which a projective cover of a module is finite direct projective cover. Additionally, we provide descriptions of modules with finite direct projective covers in the context of semi-perfect and semi-regular rings. We also discuss the properties of finite direct projective envelopes.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Finite direct projective module, semi-perfect ring, semi-regular ring.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 16D10, 16E50, 16E60, 16S50.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Finite direct projective Covers and Envelopes Sonal Gupta, Manoj Kumar Patel and Ashok Ji Gupta Department of Mathematical Sciences, IIT(BHU), Varanasi, 221005, India Department of Mathematics, National Institute of Technology Nagaland, Dimapur, 797103, India Pages 46-53 | Received 02 June 2024, Accepted 17 November 2024, 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-2634","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2634","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=2634"}],"version-history":[{"count":4,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2634\/revisions"}],"predecessor-version":[{"id":2699,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2634\/revisions\/2699"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}