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Subrings of the first neighbourhood ring: II

Published online by Cambridge University Press:  24 October 2008

D. Kirby
D. Kirby
Affiliation:
University of Southampton
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Extract

In (1) and (2) we studied a lattice of extension rings associated with a commutative ring R with identity. When R, M is a one-dimensional Cohen-Macaulay local ring the elements of are just those integral extensions of R contained in the total quotient ring T(R) and such that lengthR(S/R) is finite. Experiments with local rings of singular points on algebraic curves indicate that only the simplest singularities give rise to finite lattices. So the problem arises as to which local rings R give rise to which finite lattices. In later papers this problem will be investigated in detail, at least when R is of low embedding dimension. The purpose of the present note is to establish some general results which indicate the size of the problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 35 - 39
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Kirby, D.Subrings of the first neighbourhood ring. Math. Proc. Cambridge Phil. Soc. 86 (1979), 205–214.CrossRefGoogle Scholar
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