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

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 the commutative Noetherian ring A, and let a be an ideal of A. The A-module (0:Eα) has a secondary representation, and the finite set AttA(0:Eα) of its attached prime ideals can be formed. One of the main results of this note is that the sequence of sets (AttA(0:Eαn))n∈N is ultimately constant. This result is analogous to a theorem of M. Brodmann that, if M is a finitely generated A-module, then the sequence of sets (AssA(M/αnM))n∈N is ultimately constant.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 155 - 160
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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