Asymptotic behaviour

of certain sets of prime ideals

Authors:
Alan K. Kingsbury and Rodney Y. Sharp

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1703-1711

MSC (1991):
Primary 13E05, 13E10

MathSciNet review:
1328355

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be ideals of the commutative ring , let be a Noetherian -module and let be a submodule of ; also let be an Artinian -module and let be a submodule of . It is shown that, whenever is a sequence of -tuples of non-negative integers which is non-decreasing in the sense that for all and all , then Ass is independent of for all large , and also Att is independent of for all large . These results are proved without any regularity conditions on the ideals , and so (a special case of) the first answers in the affirmative a question raised by S. McAdam.

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Additional Information

**Alan K. Kingsbury**

Affiliation:
Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, United Kingdom

Email:
a.kingsbury@sheffield.ac.uk

**Rodney Y. Sharp**

Affiliation:
Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, United Kingdom

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

DOI:
https://doi.org/10.1090/S0002-9939-96-03400-4

Keywords:
Associated prime ideal,
attached prime ideal,
Noetherian module,
Artinian module,
asymptotic prime divisors

Received by editor(s):
December 13, 1994

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society