EXTENSIONS OF PSEUDO-VALUATIONS

Let w 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)∞i=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 Ai is a contracted ideal with respect to S, then w can be extended to S. The converse of this result is then proved. © 1969 by Pacific Journal of Mathematics.