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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- Sarah Glaz
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Email: firstname.lastname@example.org
- Received by editor(s): February 8, 2004
- Published electronically: March 31, 2005
- Communicated by: Bernd Ulrich
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2507-2513
- MSC (2000): Primary 13F05, 13D05
- DOI: https://doi.org/10.1090/S0002-9939-05-08093-7
- MathSciNet review: 2146192
Dedicated: Dedicated to Wolmer Vasconcelos