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Proceedings of the American Mathematical Society

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

 

 

Regular rings and integral extension of a regular ring


Author: Edward T. Wong
Journal: Proc. Amer. Math. Soc. 33 (1972), 313-315
MSC: Primary 16A30
MathSciNet review: 0294405
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Abstract: In this paper we show that a ring (not necessarily commutative) with identity element and without nonzero nilpotent elements is a von Neumann regular ring if every completely prime ideal is a maximal right ideal. Using this result, we show an integral extension (not necessarily commutative) without nonzero nilpotent elements of a regular ring is itself a regular ring.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294405-2
Keywords: Completely prime ideal, semicompletely prime ideal, m-system, multiplicatively closed system, regular ring, integral extension
Article copyright: © Copyright 1972 American Mathematical Society