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

 

The weak dimensions of Gaussian rings


Author: Sarah Glaz
Journal: Proc. Amer. Math. Soc. 133 (2005), 2507-2513
MSC (2000): Primary 13F05, 13D05.
Published electronically: March 31, 2005
MathSciNet review: 2146192
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Abstract: We provide necessary and sufficient conditions for a Gaussian ring $R$ to be semihereditary, or more generally, of $w.dimR\leq 1$. Investigating the weak global dimension of a Gaussian coherent ring $R$, we show that the only values $w.dimR$ may take are $0,1$ and $\infty $; but that $fP.dimR$ is always at most one. In particular, we conclude that a Gaussian coherent ring $R$ is either Von Neumann regular, or semihereditary, or non-regular of $w.dimR=\infty $.


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Additional Information

Sarah Glaz
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: glaz@uconnvm.uconn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08093-7
PII: S 0002-9939(05)08093-7
Keywords: Gaussian rings, semihereditary rings, weak dimension.
Received by editor(s): February 8, 2004
Published electronically: March 31, 2005
Dedicated: Dedicated to Wolmer Vasconcelos
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.