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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Gary F. Birkenmeier, Jin-Yong Kim and Jae Keol Park
Journal: Proc. Amer. Math. Soc. 122 (1994), 53-58
MSC: Primary 16E50; Secondary 16N40
DOI: https://doi.org/10.1090/S0002-9939-1994-1231028-7
MathSciNet review: 1231028
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1231028-7
Keywords: von Neumann regularity, prime ideal, reduced ring, Weyl algebra
Article copyright: © Copyright 1994 American Mathematical Society