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Some properties of analytically irreducible geometric quotient rings

Published online by Cambridge University Press:  24 October 2008

D. G. Northcott
D. G. Northcott
Affiliation:
St John's CollegeCambridge
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Extract

The purpose of this note is to show how a considerable part of the local theory of the prime divisors of a field of algebraic functions can be extended to analytically irreducible geometric quotient rings. In doing this we shall make frequent use of Chevalley's paper on local and semi-local rings (2). For brevity this paper will be referred to as ‘L.R.’. We begin the discussion by recalling for the reader's convenience the definition of the Kronecker product of two fields over a common subfield, since this concept will play an important role later.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 662 - 667
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Artin, E. and Whaples, G.Axiomatic characterization of fields by the product formula for valuations. Duke Math. J. 51 (1945), 469–92.Google Scholar
(2)Chevalley, C.On the theory of local rings. Ann. Math. 44 (1943), 609–708.CrossRefGoogle Scholar
(3)Schmidt, F. K.Über die Erhaltung der Kettensätze der Idealtheorie bei beliebigen endlichen Körpererweiterungen. Math. Z. 41 (1936), 443–50.CrossRefGoogle Scholar
(4)Zariski, O.Foundations of a general theory of birational correspondences. Trans. American Math. Soc. 53 (1943), 490–542.CrossRefGoogle Scholar
(5)Zariski, O.Analytical irreducibility of normal varieties. Ann. Math. 49 (1948), 352–61.CrossRefGoogle Scholar