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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The weak dimensions of Gaussian rings
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by Sarah Glaz PDF
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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Additional Information
  • Sarah Glaz
  • Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
  • Email: glaz@uconnvm.uconn.edu
  • Received by editor(s): February 8, 2004
  • Published electronically: March 31, 2005

  • Dedicated: Dedicated to Wolmer Vasconcelos
  • 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