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Factorization Rings

Published online by Cambridge University Press:  20 November 2018

J.-M. Maranda
J.-M. Maranda*
Affiliation:
Université de Montréal
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Let o be an integral domain with as field of quotients. W. Krull has shown (3 ; 4) that the following three conditions on o are equivalent:

There is a set of rank 1, discrete valuations of such that for each non-null element for all except a finite number, and such that for all if and only if for all i ∊ I.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 597 - 623
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloquium Publications, 25.Google Scholar
2. Fuchs, L., The generalization of the valuation theory, Duke Math. J., 18 (1951), 19–26.Google Scholar
3. Krull, W., Über die Zerlegung der Hauptideale in all-gemeinen Ringen, Math. Ann., 105 (1931), 1–14.Google Scholar
4. Krull, W., Idealtheorie (1935; Chelsea, 1948).Google Scholar
5. Northcott, D. G., Ideal Theory (Cambridge, 1953).Google Scholar
6. Schilling, O. F. G., The Theory of Valuations, Math. Surveys of the Amer. Math. Soc, IV (1950).Google Scholar
7. van der Waerden, B. L., Moderne Algebra (1937; 2nd ed. New York, 1943).Google Scholar