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Rank 2 valuations of K(x)

Published online by Cambridge University Press:  26 February 2010

Sudesh K. Khanduja  and
Usha Garg
Sudesh K. Khanduja
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh—160014, India.
Usha Garg
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh—160014, India.
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Let Vo 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 Vo. In this paper, we determine explicitly all rank 2 valuations of K(x) which extend Vo. 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.

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Type
Research Article
Information
Mathematika , Volume 37 , Issue 1 , June 1990 , pp. 97 - 105
Copyright
Copyright © University College London 1990

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References

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