{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:39:41Z","timestamp":1760146781388,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,10]],"date-time":"2024-12-10T00:00:00Z","timestamp":1733788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Doctoral\/High-level Talents Research Foundation of Jinling Institute of Technology","award":["jit-b-202043"],"award-info":[{"award-number":["jit-b-202043"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The regularity of the n-P-V-rings and n-P-V\u2019-rings is systematically investigated in this paper. Employing the notions of quasi-ideals, weakly left (or right) ideals, and generalized weak ideals, we focus on investigating the strong \u03c0-regularity and weak \u03c0-regularity of the n-P-V-rings and the n-P-V\u2019-rings. Subsequently, we demonstrate our results as follows: (1) R is strongly \u03c0-regular if R is a left n-P-V-ring where all its maximal left ideals are either quasi-ideals, weakly right ideals, or generalized weak ideals. (2) R is strongly \u03c0-regular iff R is an abelian left (right) n-P-V\u2019-ring where all its maximal essential left (right) ideals are either quasi-ideals, weakly right (left) ideals, or generalized weak ideals. (3) R is reduced left weakly \u03c0-regular if R is an idempotent reflexive semi-abelian left n-P-V\u2019-ring where all its maximal essential left ideals are either quasi-ideals, weakly right ideals, or generalized weak ideals.<\/jats:p>","DOI":"10.3390\/axioms13120863","type":"journal-article","created":{"date-parts":[[2024,12,10]],"date-time":"2024-12-10T11:17:20Z","timestamp":1733829440000},"page":"863","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Regularity of n-P-V-Rings and n-P-V\u2019-Rings"],"prefix":"10.3390","volume":"13","author":[{"given":"Liuwen","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Jinling Institute of Technology, Nanjing 211169, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenlin","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10468-011-9276-4","article-title":"Rings of idempotent stable range one","volume":"15","author":"Wang","year":"2012","journal-title":"Algebras Represent. 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Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/12\/863\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:51:37Z","timestamp":1760115097000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/12\/863"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,10]]},"references-count":16,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["axioms13120863"],"URL":"https:\/\/doi.org\/10.3390\/axioms13120863","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,12,10]]}}}