Abstract
Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. Key words and phrases. integral closure, reduction of an ideal, reduction of a module, reduction number, Rees algebra.
| Original language | English |
|---|---|
| Pages (from-to) | 3823-3831 |
| Number of pages | 9 |
| Journal | Communications in Algebra |
| Volume | 27 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1999 Jan 1 |
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ASJC Scopus subject areas
- Algebra and Number Theory
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Reduction number one for finitely generated torsion-free modules. / Liu, Jung Chen.
In: Communications in Algebra, Vol. 27, No. 8, 01.01.1999, p. 3823-3831.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Reduction number one for finitely generated torsion-free modules
AU - Liu, Jung Chen
PY - 1999/1/1
Y1 - 1999/1/1
N2 - Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. Key words and phrases. integral closure, reduction of an ideal, reduction of a module, reduction number, Rees algebra.
AB - Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. Key words and phrases. integral closure, reduction of an ideal, reduction of a module, reduction number, Rees algebra.
UR - http://www.scopus.com/inward/record.url?scp=0033411983&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033411983&partnerID=8YFLogxK
U2 - 10.1080/00927879908826666
DO - 10.1080/00927879908826666
M3 - Article
AN - SCOPUS:0033411983
VL - 27
SP - 3823
EP - 3831
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 8
ER -