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Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings II

Published online by Cambridge University Press:  20 January 2009

H. Ansari Toroghy  and
R. Y. Sharp
H. Ansari Toroghy
Affiliation:
Department of Pure MathematicsUniversity of SheffieldHicks BuildingSheffield S3 7RH
R. Y. Sharp
Affiliation:
Department of Pure MathematicsUniversity of SheffieldHicks BuildingSheffield S3 7RH
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Abstract

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Let E be an injective module over a commutative Noetherian ring A (with non-zero identity), and let a be an ideal of A. The submodule (0:Eα) of E has a secondary representation, and so we can form the finite set AttA(0:Eα) of its attached prime ideals. In [1, 3.1], we showed that the sequence of sets is ultimately constant; in [2], we introduced the integral closure a*(E) of α relative to E, and showed that is increasing and ultimately constant. In this paper, we prove that, if a contains an element r such that rE = E, then is ultimately constant, and we obtain information about its ultimate constant value.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 511 - 518
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

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