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Valuations of polynomial rings

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Title: Valuations of polynomial rings
Author: Macauley, Ronald Alvin
Degree Master of Arts - MA
Program Mathematics
Copyright Date: 1951
Subject Keywords Polynomials
Abstract: If R is a field on which all (non-archimedean) valuations are known, then all valuations on R[x], where x is transcendental over R , are also known. Ostrowski described such valuations of R[x] by means of pseudo-convergent sequences in the algebraic completion of A of R . MacLane later showed that if all valuations of R are discrete, then any valuation V of R [x] can be represented by certain "key" polynomials in R [x]. The present paper exhibits the connection between these two treatments. This is achieved by first determining keys for the valuation which a pseudo-convergent sequence defines on A[x], and then relating these keys to those for V .
URI: http://hdl.handle.net/2429/41331
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

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