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Pseudovaluations of Polynomials

Published online by Cambridge University Press:  20 November 2018

R. Nelson
R. Nelson*
Affiliation:
Queen's University, Belfast
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A valuation of a ring K is a function

where A is an archimedean ordered field and W has the properties of the absolute valuation; see (2, chap. X). The theory was extended in 1936 by K. Mahler (1), who introduced the concept of pseudovaluations. Whereas for a valuation we must always have

for a pseudovaluation it is sufficient that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1293 - 1302
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Mahler, K., Über Pseudobewertungen, I, Acta Math., 66 (1936), 79–119.Google Scholar
2. Van der Waerden, B. L., Modern algebra, Vol. 1 (Berlin, 1949).Google Scholar