Bishnoi, Anuj ; Khanduja, Sudesh K. (1990) Rank 2 valuations of K (x) Mathematika, 37 (1). pp. 97-105. ISSN 0025-5793
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Official URL: http://journals.cambridge.org/action/displayAbstra...
Related URL: http://dx.doi.org/10.1112/S0025579300012833
Abstract
Let V0 be a discrete real valuation of a field K and x an indeterminate. In 1936, MacLane [3] gave a method of constructing all real valuations of K(x) which are extensions of V0.In this paper, we determine explicitly all rank 2 valuations of K(x) which extend V0.One can thereby describe all rank 2 valuations of K(x, y) which are trivial on an arbitrary K; x, y being algebraically independent over the field K. The latter valuations have been considered by Zariski [5] in the case when K is an algebraically closed field of characteristic zero.
Item Type: | Article |
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ID Code: | 69910 |
Deposited On: | 17 Nov 2011 03:37 |
Last Modified: | 17 Nov 2011 03:37 |
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