Primary decomposition: Compatibility, independence and linear growth
Author:
Yongwei Yao
Journal:
Proc. Amer. Math. Soc. 130 (2002), 16291637
MSC (2000):
Primary 13E05; Secondary 13C99, 13H99
Published electronically:
November 15, 2001
MathSciNet review:
1887009
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Abstract: For finitely generated modules over a Noetherian ring , we study the following properties about primary decomposition: (1) The Compatibility property, which says that if and is a primary component of for each , then ; (2) For a given subset , is an open subset of if and only if the intersections for all possible primary components and of ; (3) A new proof of the `Linear Growth' property, which says that for any fixed ideals of there exists a such that for any there exists a primary decomposition of such that every primary component of that primary decomposition contains .
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Additional Information
Yongwei Yao
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email:
yyao@math.ukans.edu
DOI:
http://dx.doi.org/10.1090/S0002993901062840
PII:
S 00029939(01)062840
Keywords:
Primary decomposition,
Linear Growth,
ArtinRees number
Received by editor(s):
October 5, 2000
Received by editor(s) in revised form:
January 12, 2001
Published electronically:
November 15, 2001
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2001
American Mathematical Society
