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Artinian modules over commutative rings

Published online by Cambridge University Press:  24 October 2008

R. Y. Sharp
R. Y. Sharp
Affiliation:
Department of Pure Mathematics, The University, Sheffield S3 7RH
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Extract

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring R (throughout the paper, R will denote a commutative ring with identity) can, for some purposes at least, be reduced to the study of an Artinian module A' over a complete (Noetherian) local ring; in the latter situation, Matlis' duality 1 (alternatively, see 6, ch. 5) is available, and this means that the investigation can often be converted into a dual one about a finitely generated module over a complete (Noetherian) local ring.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 25 - 33
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

1Matlis, E.. Injective modules over Noetherian rings. Pacific J. Math. 8 (1958), 511528.CrossRefGoogle Scholar
2Matsumura, H.Commutative Ring Theory (Cambridge University Press, 1986).Google Scholar
3Northcott, D. G.. An Introduction to Homological Algebra (Cambridge University Press, 1960).CrossRefGoogle Scholar
4Northcott, D. G.. Lessons on Rings, Modules and Multiplicities (Cambridge University Press, 1968).CrossRefGoogle Scholar
5Sharp, R. Y.. A method for the study of Artinian modules, with an application to asymptotic behavior. In Commutative Algebra Proceedings of a Microprogram held June 15July 2, 1987. Mathematical Sciences Research Institute Publications no. 15 (Springer-Verlag, 1989), pp. 443465.CrossRefGoogle Scholar
6Sharpe, D. W. and Vmos, P.Injective Modules (Cambridge University Press, 1972).Google Scholar
7Zariski, O. and Samuel, P.Commutative Algebra, vol. II. Graduate Texts in Math. no. 29 (Springer-Verlag, 1975).Google Scholar