Extensions of pseudo-valuations

Abstract

Let o be a pseudo-valuation defined on a commutative ring R and let S be an overring of R. This paper investigates conditions needed to imply that w can be extended to S. These conditions are given in terms of a particular sequence of ideals {Ai)T=o in R which is called the best filtration for w. The main theorem states that if w is a pseudo-valuation on R with best filtration {Ai} and each A% is a contracted ideal with respect to S, then w can be extended to S. The converse of this result is then proved.