Injective modules and linear growth of primary decompositions |
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Authors: | R. Y. Sharp |
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Affiliation: | Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom |
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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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Keywords: | Commutative Noetherian ring primary decomposition associated prime ideal injective module Artin-Rees Lemma |
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