Vol. 29, No. 2, 1969

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Extensions of pseudo-valuations

James A. Huckaba

Vol. 29 (1969), No. 2, 295–302

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=0 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.

Mathematical Subject Classification
Primary: 13.98
Received: 10 June 1968
Published: 1 May 1969
James A. Huckaba