Injective modules and linear growth

of primary decompositions

Author:
R. Y. Sharp

Journal:
Proc. Amer. Math. Soc. **128** (2000), 717-722

MSC (1991):
Primary 13E05

Published electronically:
October 6, 1999

MathSciNet review:
1641105

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Abstract | References | Similar Articles | Additional Information

Abstract: The purposes of this paper are to generalize, and to provide a short proof of, I. Swanson's Theorem that each proper ideal in a commutative Noetherian ring has linear growth of primary decompositions, that is, there exists a positive integer such that, for every positive integer , there exists a minimal primary decomposition with for all . The generalization involves a finitely generated -module and several ideals; the short proof is based on the theory of injective -modules.

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Additional Information

**R. Y. Sharp**

Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom

Email:
r.y.sharp@sheffield.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05170-9

Keywords:
Commutative Noetherian ring,
primary decomposition,
associated prime ideal,
injective module,
Artin-Rees Lemma

Received by editor(s):
May 5, 1998

Published electronically:
October 6, 1999

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1999
American Mathematical Society