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Krull dimension and generalized fractions

Published online by Cambridge University Press:  20 January 2009

M. A. Hamieh
Affiliation:
Department of Purec Mathematics, University of Sheffield, Sheffield S3 7RH
R. Y. Sharp
Affiliation:
Department of Purec Mathematics, University of Sheffield, Sheffield S3 7RH
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Let R be a (commutative Noetherian) local ring (with identity) having maximal ideal and dimension d≧l. It is shown in [5,3.6rsqb; that the local cohomology module may be described as a module of generalized fractions: if x1…,xd is a system of parameters for R, then , where U(x)d+1 is the triangular subset [4,2.1] of Rd+1 given by

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Grothendieck, A., Local cohomology (Lecture Notes in Mathematics 41, Springer, Berlin, 1967).Google Scholar
2.Macdonald, I. G. and Sharp, R. Y., An elementary proof of the non-vanishing of certain local cohomology modules, Quart. J. Math. Oxford (2), 23 (1972), 197204.CrossRefGoogle Scholar
3.O'Carroll, L., On the generalized fractions of Sharp and Zakeri, J. London Math. Soc. (2), 28 (1983), 417427.CrossRefGoogle Scholar
4.Sharp, R. Y. and Zakeri, H., Modules of generalized fractions, Mathematika, 29 (1982), 3241.CrossRefGoogle Scholar
5.Sharp, R. Y. and Zakeri, H., Local cohomology and modules of generalized fractions, Mathematika, 29 (1982), 296306.CrossRefGoogle Scholar
6.Sharp, R. Y. and Zakeri, H., Modules of generalized fractions and balanced big Cohen-Macaulay modules, Commutative algebra: Durham 1981 (London Mathematical Society Lecture Notes 72, ed. Sharp, R. Y., Cambridge University Press, Cambridge, 1982), pp. 6182.Google Scholar