J. Korean Math. Soc. 2016; 53(1): 217-232
Printed January 1, 2016
https://doi.org/10.4134/JKMS.2016.53.1.217
Copyright © The Korean Mathematical Society.
Juncheol Han, Yang Lee, Sangwon Park, Hyo Jin Sung, and Sang Jo Yun
Pusan National University, Pusan National University, Dong-A University, Pusan National University, Pusan National University
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 {\it 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 {\it 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
MSC numbers: 16E50, 16S50
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