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 . / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/41331 |
| Date | January 1951 |
| Creators | Macauley, Ronald Alvin |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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