Asymptotic behaviour of certain sets of prime ideals
Authors:
Alan K. Kingsbury and Rodney Y. Sharp
Journal:
Proc. Amer. Math. Soc. 124 (1996), 17031711
MSC (1991):
Primary 13E05, 13E10
MathSciNet review:
1328355
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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 nonnegative integers which is nondecreasing 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:
http://dx.doi.org/10.1090/S0002993996034004
PII:
S 00029939(96)034004
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
