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Integral closures of ideals relative to Artinian modules, and exact sequences

Published online by Cambridge University Press:  18 May 2009

R. Y. Sharp  and
Y. Tiraş
R. Y. Sharp
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7Rh
Y. Tiraş
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7Rh
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In [3], Sharp and Taherizadeh introduced concepts of reduction and integral closure of an ideal I of a commutative ring R (with identity) relative to an Artinian R-module A, and they showed that these concepts have properties which reflect some of those of the classical concepts of reduction and integral closure introduced by Northcott and Rees in [2].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 103 - 107
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Kirby, D., Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford Ser. (2) 24 (1973), 47–57.CrossRefGoogle Scholar
2.Northcott, D. G. and Rees, D., Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158.CrossRefGoogle Scholar
3.Sharp, R. Y. and Taherizadeh, A.-J., Reductions and integral closures of ideals relative to an Artinian module, J. London Math. Soc. (2) 37 (1988), 203–218.Google Scholar
4.Sharp, R. Y., Tiras, Y., and Yassi, M., Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings, J. London Math. Soc. (2) 42 (1990), 385–392.Google Scholar
5.Sharpe, D. W. and Vdmos, P., Injective modules (Cambridge University Press, 1972).Google Scholar