The weak dimensions of Gaussian rings

Glaz, Sarah

doi:10.1090/S0002-9939-05-08093-7

The weak dimensions of Gaussian rings
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Proc. Amer. Math. Soc. 133 (2005), 2507-2513 Request permission

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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