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Keywords = left weakly π-regular

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12 pages, 222 KB  
Article
Regularity of n-P-V-Rings and n-P-V’-Rings
by Liuwen Li, Wenlin Zou and Ying Li
Axioms 2024, 13(12), 863; https://doi.org/10.3390/axioms13120863 - 10 Dec 2024
Viewed by 887
Abstract
The regularity of the n-P-V-rings and n-P-V’-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 π-regularity and weak π-regularity of the n-P-V-rings and [...] Read more.
The regularity of the n-P-V-rings and n-P-V’-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 π-regularity and weak π-regularity of the n-P-V-rings and the n-P-V’-rings. Subsequently, we demonstrate our results as follows: (1) R is strongly π-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 π-regular iff R is an abelian left (right) n-P-V’-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 π-regular if R is an idempotent reflexive semi-abelian left n-P-V’-ring where all its maximal essential left ideals are either quasi-ideals, weakly right ideals, or generalized weak ideals. Full article
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