[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2016.53.1.217

ON IDEMPOTENTS IN RELATION WITH REGULARITY

HAN, JUNCHEOL (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
LEE, YANG (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
PARK, SANGWON (DEPARTMENT OF MATHEMATICS DONG-A UNIVERSITY)
SUNG, HYO JIN (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
YUN, SANG JO (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 217-232 More about this Journal

Abstract

We make a study of two generalizations of regular rings, concentrating our attention on the structure of idempotents. A ring R is said to be right attaching-idempotent if for $a{\in}R$ there exists $0{\neq}b{\in}R$ such that ab is an idempotent. Next R is said to be generalized regular if for $0{\neq}a{\in}R$ there exist nonzero $b{\in}R$ such that ab is a nonzero idempotent. It is first checked that generalized regular is left-right symmetric but right attaching-idempotent is not. The generalized regularity is shown to be a Morita invariant property. More structural properties of these two concepts are also investigated.

Keywords

generalized regular ring; (von Neumann) regular ring; Morita invariant; idempotent; strongly (generalized) regular ring; reduced ring; Abelian ring;

Citations & Related Records

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