ON IDEMPOTENTS IN RELATION WITH REGULARITY

Title & Authors
ON IDEMPOTENTS IN RELATION WITH REGULARITY
HAN, JUNCHEOL; LEE, YANG; PARK, SANGWON; SUNG, HYO JIN; YUN, SANG JO;

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 $\small{a{\in}R}$ there exists $\small{0{\neq}b{\in}R}$ such that ab is an idempotent. Next R is said to be generalized regular if for $\small{0{\neq}a{\in}R}$ there exist nonzero $\small{b{\in}R}$ 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;
Language
English
Cited by
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