{"id":2932,"date":"2026-01-03T20:25:08","date_gmt":"2026-01-03T20:25:08","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2932"},"modified":"2026-01-26T12:05:50","modified_gmt":"2026-01-26T12:05:50","slug":"on-phi-gorenstein-homological-dimensions","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-phi-gorenstein-homological-dimensions\/","title":{"rendered":"On $\\phi$-Gorenstein homological dimensions"},"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 \\phi<\/span>-Gorenstein homological dimensions<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Younes El Haddaoui\\,^1<\/span>, Hwankoo Kim<\/strong>\\,^2<\/span><\/i> and Najib Mahdou\\,^3<\/span>
\\,^{1,3}<\/span> Department of Mathematics, Faculty of Science and Technology, Fez, Morocco.
\\,^{2}<\/span> Division of Computer Engineering, Hoseo University, Asan, Republic of Korea.<\/p>\n\n\n\n


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Pages 176-197 | Received 20 November 2024, Accepted 28 February 2025, Published 26 January 2026 <\/span><\/p>\n\n\n\n

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

The study of Gorenstein projective and injective modules has been a cornerstone in the field of Gorenstein homological algebra since these concepts were first introduced. This paper marks a significant advancement in the field by demonstrating the integration of \\phi<\/span>-torsion theory into Gorenstein homological algebra. We take this exploration further by introducing and examining the novel concepts of nonnil-Gorenstein projective and injective modules. Our study also extends to the nonnil-Gorenstein projective and injective dimensions of a module, offering a deeper insight into their structure and implications. Furthermore, we delve into the concept of nonnil-Gorenstein global dimension of a ring, unveiling its significance and potential applications. A key application of these innovative concepts is their use in characterizing \\phi<\/span>-von Neumann regular rings. This approach not only adds a new dimension to our understanding of these rings but also highlights the versatility and depth of Gorenstein homological algebra.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span> \\phi<\/span>-torsion theory, \\phi<\/span>-(weak) global dimension of rings, nonnil-Gorenstein global dimension of rings.<\/p>\n\n\n\n

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MSC numbers<\/strong>:<\/span> 13A15, 13A18, 13F05, 13G05, 13C20.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On -Gorenstein homological dimensions Younes El Haddaoui, Hwankoo Kim and Najib Mahdou Department of Mathematics, Faculty of Science and Technology, Fez, Morocco. Division of Computer Engineering, Hoseo University, Asan, Republic of Korea. Pages 176-197 | Received 20 November 2024, Accepted 28 February 2025, Published 26 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-2932","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2932","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=2932"}],"version-history":[{"count":4,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2932\/revisions"}],"predecessor-version":[{"id":2997,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2932\/revisions\/2997"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}