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J. Korean Math. Soc. 2012; 49(3): 605-622
Printed May 1, 2012
https://doi.org/10.4134/JKMS.2012.49.3.605
Copyright © The Korean Mathematical Society.
Rings close to semiregular
P\i nar Aydo\u gdu, Yang Lee, and A. \c{C}i\u {g}dem \"{O}zcan
Hacettepe University, Pusan National University, Hacettepe University
A ring $R$ is called semiregular if $R/J$ is regular and idempotents lift modulo $J$,where $J$ denotes the Jacobson radical of $R$. We give some characterizations of rings $R$ such that idempotents lift modulo $J$, and $R/J$ satisfies one of the following conditions: (one-sided) unit--regular, strongly regular, (unit, strongly, weakly) $\pi$--regular.
Keywords: idempotent lifting, semi unit-regular ring, semi (strongly) $\pi$-regular ring
MSC numbers: 16E50, 16U99
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