A connection between weak regularity and the simplicity of prime factor rings

Birkenmeier, Gary F.; Kim, Jin-Yong; Park, Jae Keol

doi:10.1090/S0002-9939-1994-1231028-7

A connection between weak regularity and the simplicity of prime factor rings
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by Gary F. Birkenmeier, Jin-Yong Kim and Jae Keol Park PDF

Proc. Amer. Math. Soc. 122 (1994), 53-58 Request permission

Abstract:

In this paper, we show that a reduced ring R is weakly regular (i.e., ${I^2} = I$ for each one-sided ideal I of R) if and only if every prime ideal is maximal. This result extends several well-known results. Moreover, we provide examples which indicate that further generalization of this result is limited.

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