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.
Gaussian properties of total rings of quotients
BAZZONI, SILVANA;
2007
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.
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