F-rational rings and the integral closures of ideals. II (Q2741181)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: F-rational rings and the integral closures of ideals. II |
scientific article; zbMATH DE number 1642427
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | F-rational rings and the integral closures of ideals. II |
scientific article; zbMATH DE number 1642427 |
Statements
18 August 2002
0 references
integral closure
0 references
tight closure
0 references
characteristic \(p\)
0 references
F-rational rings
0 references
F-regular rings
0 references
history of the Briançon-Skoda theorems
0 references
0.9820972
0 references
0 references
0 references
0.8974861
0 references
0 references
0.8938019
0 references
F-rational rings and the integral closures of ideals. II (English)
0 references
[For part I of this paper see \textit{I. M. Aberbach} and \textit{C. Huneke}, Mich. Math. J. 49, No. 1, 3-11 (2001; Zbl 1016.13003).]NEWLINENEWLINENEWLINEThe main results are new extensions of the Briançon-Skoda theorem with coefficients for F-rational rings. These currently best versions for F-rational rings are still weaker than the known versions for regular rings. The main methods of the proofs come from the theory of tight closure. The last section contains a version of the cancellation theorem for Cohen-Macaulay rings. Corollaries are further versions of the Briançon-Skoda theorem for excellent weakly F-regular rings. NEWLINENEWLINENEWLINEThe second section of the paper gives a comprehensive history of the Briançon-Skoda theorems.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00058].
0 references
