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The product of n linear forms in a field of series

Published online by Cambridge University Press:  26 February 2010

J. V. Armitage
J. V. Armitage
Affiliation:
67 Haigh Road, Rothwell, Leeds.
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Extract

Let K be a field. We denote by K[t] the integral domain of all polynomials in an indeterminate t with coefficients in K, and by K(t) the quotient field of K[t], i.e. the field of all formal rational functions of t over K. A valuation |f| of the elements f of K(t) can be defined by

for f ≠ 0, and |0| = 0, where e > 1. This valuation is multiplicative, and has the properties

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 132 - 137
Copyright
Copyright © University College London 1957

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References

page 132 note † The substance of this paper formed part of the author's Ph.D. thesis (London, 1956).

page 132 note ‡ Mahler, K., Annals of Math., 42 (1941), 488–522.CrossRefGoogle Scholar

page 135 note † See Perron, Algebra I (1st ed.), p. 82, Theorem 75.