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Quasi-finite modules and asymptotic prime divisors

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Title Quasi-finite modules and asymptotic prime divisors
 
Creator KATZ, D
PUTHENPURAKAL, TJ
 
Subject Quasi-finite modules
Multigraded modules
Asymptotic prime divisors
MULTIGRADED MODULES
IDEALS
POWERS
STABILITY
 
Description Let A be a Noetherian ring, J subset of A an ideal and C a finitely generated A-module. In this note we would like to prove the following statement. Let {I-n}(n >= 0) be a collection of ideals satisfying: (i) I-n superset of J(n), for all n, (ii) J(s) . I-s subset of Ir+s, for all r,s >= 0 and (iii) I-n subset of I-m, whenever m = 1) Ass(A)(InC/J(n)C) is finite, so the issue at hand is the realization that the primes in Ass(A)(InC/J(n)C) do not behave periodically, as one might have expected, say if circle plus(n >= 0) I-n were a Noetherian A-algebra generated in degrees greater than one. We also give a multigraded version of our results. (C) 2013 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2014-10-16T06:49:40Z
2014-10-16T06:49:40Z
2013
 
Type Article
 
Identifier JOURNAL OF ALGEBRA, 38018-29
http://dx.doi.org/10.1016/j.jalgebra.2013.01.024
http://dspace.library.iitb.ac.in/jspui/handle/100/15476
 
Language en