Go to  Advanced Search

Valuations of polynomial rings

Show full item record

Files in this item

Files Size Format Description   View
UBC_1951_A8 M23 V2.pdf 2.250Mb Adobe Portable Document Format   View/Open
Title: Valuations of polynomial rings
Author: Macauley, Ronald Alvin
Degree: Master of Arts - MA
Program: Mathematics
Copyright Date: 1951
Subject Keywords Polynomials
Issue Date: 2012-03-09
Publicly Available in cIRcle 2012-03-10
Publisher University of British Columbia
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
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 .
Affiliation: Science, Faculty of
URI: http://hdl.handle.net/2429/41331
Scholarly Level: Graduate

This item appears in the following Collection(s)

Show full item record

UBC Library
1961 East Mall
Vancouver, B.C.
Canada V6T 1Z1
Tel: 604-822-6375
Fax: 604-822-3893