Journal article
The krull intersection theorem
Pacific Journal of Mathematics, Vol.57(1), pp.11-14
1975
DOI: 10.2140/pjm.1975.57.11
Abstract
Let R be a commutative ring, I an ideal in R, and A an R-module. We always have (FORMULA PRESENTED) InA where S is the multiplicatively closed set (FORMULA PRESENTED) and (FORMULA PRESENTED). It is of interest to know when some containment can be replaced by equality. The Krull intersection theorem states that for R Noetherian and A finitely generated (FORMULA PRESENTED). Since (FORMULA PRESENTED) is finitely generated, (FORMULA PRESENTED). Thus if I E rad (R), the Jacobson radical of R, or R is a domain and A is torsion- free, we have (FORMULA PRESENTED). In this note we show that for a Priifer domain R and a torsion-free i?-module A, (FORMULA PRESENTED). We also consider the condition (*): (FORMULA PRESENTED) for every ideal I in the commutative ring R. It is shown that a polynomial ring in any set of indeterminants over a Noetherian domain and the integral closure of a Noetherian domain satisfy (*). © 1975 Pacific Journal of Mathematics. All Rights Reserved.
Details
- Title: Subtitle
- The krull intersection theorem
- Creators
- Daniel D Anderson
- Resource Type
- Journal article
- Publication Details
- Pacific Journal of Mathematics, Vol.57(1), pp.11-14
- DOI
- 10.2140/pjm.1975.57.11
- ISSN
- 0030-8730
- Language
- English
- Date published
- 1975
- Academic Unit
- Mathematics
- Record Identifier
- 9984230419202771
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