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Some results concerning the local analytic branches of an algebraic variety

Published online by Cambridge University Press:  24 October 2008

D. G. Northcott
D. G. Northcott
Affiliation:
Sheffield University
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Extract

The recent progress of modern algebra in analysing, from the algebraic standpoint, the foundations of algebraic geometry, has been marked by the rapid development of what may be called ‘analytic algebra’. By this we mean the topological theories of Noetherian rings that arise when one uses ideals to define neighbourhoods; this includes, for instance, the theory of power-series rings and of local rings. In the present paper some applications are made of this kind of algebra to some problems connected with the notion of a branch of a variety at a point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 3 , July 1953 , pp. 386 - 396
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Chevalley, C.On the theory of local rings. Ann. Math., Princeton (2), 44 (1943), 690–708.CrossRefGoogle Scholar
(2)Chevalley, C.Some properties of ideals in rings of power series. Trans. Amer. math. Soc. 55 (1944), 68–84.CrossRefGoogle Scholar
(3)Chevalley, C.Intersections of algebraic and algebroid varieties. Trans. Amer. math. Soc. 57 (1945), 1–85.CrossRefGoogle Scholar
(4)Cohen, I. S.On the structure and ideal theory of complete local rings. Trans. Amer. math. Soc. 59 (1946), 54–106.CrossRefGoogle Scholar
(5)Northcott, D. G.The number of analytic branches of a variety. J. Lond. math. Soc. 25 (1950), 275–9.CrossRefGoogle Scholar
(6)Northcott, D. G.Some properties of analytically irreducible geometric quotient rings. Proc. Camb. phil. Soc. 47 (1951), 662–7.CrossRefGoogle Scholar
(7)Zariski, O.Analytical irreducibility of normal varieties. Ann. Math., Princeton, (2), 49 (1948), 352–61.CrossRefGoogle Scholar
(8)Zariski, O.Sur la normalité analytique des variétés normales. Ann. Inst. Fourier, 2 (1950), 161–4.CrossRefGoogle Scholar