On weak $Pi$-regularity and the simplicity of prime factor rings
Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 151-156 Printed March 1, 2007
Jin Yong Kim and Hai Lan Jin Kyung Hee University, Yanbian University
Abstract : A connection between weak $\pi$-regularity and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring $R$ is weakly $\pi$-regular if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.
Keywords : completely prime ideals, 2-primal rings, weakly $\pi$-regular rings, pseudo symmetric rings, minimal prime ideals