Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T01:07:23.201Z Has data issue: false hasContentIssue false
  • English
  • Français

Subrings of the first neighbourhood ring

Published online by Cambridge University Press:  24 October 2008

D. Kirby
D. Kirby
Affiliation:
University of Southampton
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. In (2) we associated with a commutative ring R with identity the lattice ℒ(R) of rings S which satisfy (i) R ⊆ S ⊆ T, where T is the total quotient ring of R, and (ii) dS ⊆ R for some d ∈ R which is not a zero-divisor. The rings of ℒ(R) can be constructed by blowing up ideals of the set of ideals A of R which satisfy (i) 0: A = 0, and (ii) there exist integers m1n ≥ 1 and α ∈ An such that αAm = Am+n (see Propositions 2·3 and 2·5 of (2)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 205 - 214
Copyright
Copyright © Cambridge Philosophical Society 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bass, H.On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–28.CrossRefGoogle Scholar
(2)Kirby, D. and Adranghi, M. R.A lattice of extension rings for a commutative ring. Math. Proc. Camb. Phil. Soc. 84 (1978), 226–234.CrossRefGoogle Scholar
(3)Matlis, E.The multiplicity and reduction number of a one-dimensional local ring. Proc. London Math. Soc. 26 (1973), 273–288.CrossRefGoogle Scholar
(4)Northcott, D. G.Hilbert's function in a local ring. Quart. J. Math. Oxford Ser. (2) 4 (1953), 67–80.CrossRefGoogle Scholar
(5)Northcott, D. G.The reduction number of a one-dimensional local ring. Mathematika 6 (1959), 87–90.CrossRefGoogle Scholar