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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embeddings of the maximal quotient ring of a von Neumann regular ring into its completion with respect to a rank function


Author: Annie Vogel
Journal: Proc. Amer. Math. Soc. 102 (1988), 480-482
MSC: Primary 16A30; Secondary 16A08, 16A52
MathSciNet review: 928964
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Abstract: Let $ R$ be a commutative von Neumann regular ring. A pseudorank function on $ R$ is characterized by a probability measure on the spectrum of $ R$. We exhibit two commutative von Neumann regular rings $ R$ and $ R'$ with the same spectrum $ S$, and two rank functions $ N$ and $ N'$ on $ R$ and $ R'$, corresponding to the same probability measure on $ S$, and such that the maximal right quotient ring $ {Q_{\max }}(R)$ embeds in the $ N$-completion $ \bar R$ of $ R$ while $ {Q_{\max }}(R')$ does not embed in $ \overline {R'} $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0928964-2
PII: S 0002-9939(1988)0928964-2
Keywords: Von Neumann regular ring, $ N$-completion, maximal quotient ring
Article copyright: © Copyright 1988 American Mathematical Society