ON RIGHT QUASI-DUO RINGS WHICH ARE II-REGULAR

• Kim, Nam-Kyun (Department of Mathematics, Kyung Hee University) ;
• Lee, Yang (Department of Mathematics Education, Pusan National University)
• Published : 2000.05.01
• 72 6

Abstract

This paper is motivated by the results in [2], [10], [13] and [19]. We study some properties of generalizations of commutative rings and relations between them. We also show that for a right quasi-duo right weakly ${\pi}-regular$ ring R, R is an (S,2)-ring if and only if every idempotent in R is a sum of two units in R, which gives a generalization of [2, Theorem 4] on right quasi-duo rings. Moreover we find a condition which is equivalent to the strongly ${\pi}-regularity$ of an abelian right quasi-duo ring.

Keywords

quasi-duo ring;${\pi}-regular$ ring;(S, 2)-ring and 2-primal ring

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