Holder valuation and holder rigidity for right ring of fractions

Abstract

The purpose of this article is to introduce the notion of (C1,C2)-Holder Krull valuation on right ring of fractions ( with respect to right denominator set S in a ring R). It is proved that if R is a ring satisfying in Holder rigidity condition, and S a right permutable set of regular elements in R, then the right ring of fractions R′= Q Â(R) with respect to S satisfies in H¨older rigidity condition. This results provide an extension of the Garsia theorem (see [2]) for right ring of fractions.