Gaussian properties of total rings of quotients

By Silvana Bazzoni, Sarah Glaz. 2007

75 citations recorded by the source corpus.

Abstract In this paper we consider five possible extensions of the Prufer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients. We show that a Prufer ring R satisfies one of the five conditions if and only if the total ring of quotients Q ( R ) of R satisfies that same condition. We focus in particular on the Gaussian property of a ring.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e5e75b419841a706a48aa3878e18a5d18893f940

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In Algebra and Number Theory

1. S. Kabbaj
2. Najib Mahdou
3. Driss Bennis

In Geometry and Topology

1. Najib Mahdou
2. Driss Bennis

Citations in the corpus

• Trivial extensions defined by Prüfer conditions (2008, background): “In particular, we obtain further evidence for the validity of Bazzoni–Glaz conjecture sustaining that ‘‘the weak global dimension of a Gaussian ring is 0, 1, or∞’’ [3].”