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Abstract dilatations and infinitely near points

Published online by Cambridge University Press:  24 October 2008

D. G. Northcott
D. G. Northcott
Affiliation:
The UniversitySheffield
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Extract

In the following pages there is developed an abstract theory of infinitely near points for two-dimensional regular local rings which have infinite residue fields. The scope of the theory may be indicated by the fact that it contains generalizations of Noether's formula for intersection multiplicities (Theorem 8), the theory of proximate points (§ 8) and the conditions for a set of integers to be curve multiplicities at a given finite sequence of consecutive points (§ 10). To this extent our account resembles that given by van der Waerden ((6), Chap. 9), but the starting point and (with the exception of the concluding section) the type of reasoning employed are very different. There is also a marked contrast with the methods used by Zariski (7) in an account of related topics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 178 - 197
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

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(5)Northcott, D. G. On the algebraic foundations of the theory of local dilatations. Proc. Lond. math. Soc. (to appear).Google Scholar
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