Regular rings and integral extension of a regular ring
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- by Edward T. Wong PDF
- Proc. Amer. Math. Soc. 33 (1972), 313-315 Request permission
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.References
- V. A. Andrunakievič and Ju. M. Rjabuhin, Rings without nilpotent elements, and completely prime ideals, Dokl. Akad. Nauk SSSR 180 (1968), 9–11 (Russian). MR 0230760
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 313-315
- MSC: Primary 16A30
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294405-2
- MathSciNet review: 0294405