Primary decomposition: Compatibility, independence and linear growth

Author:
Yongwei Yao

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1629-1637

MSC (2000):
Primary 13E05; Secondary 13C99, 13H99

DOI:
https://doi.org/10.1090/S0002-9939-01-06284-0

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:
https://doi.org/10.1090/S0002-9939-01-06284-0

Keywords:
Primary decomposition,
Linear Growth,
Artin-Rees 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