The tight integral closure of a set of ideals. (English) Zbl 0966.13003
The author introduces the notion of tight integral closure of a set of ideals. This is a notion that combines integral and tight closures. Hochster presents its theory with illuminating comparisons with the two other closures. The main result is a new generalization of the Briançon-Skoda theorem. Some of the other results are about integral tight closure in one-dimensional Noetherian rings and in complete tensor products. The paper also contains examples of Miller and Singh of tight integral closure in polynomial rings. At the end there is an overview of open questions about tight integral closure.
Reviewer: Irena Swanson (Las Cruces)
MSC:
| 13B22 | Integral closure of commutative rings and ideals |
| 13A35 | Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure |
Keywords:
tight integral closure of a set of ideals; Briançon-Skoda theorem; one-dimensional Noetherian rings; complete tensor products; polynomial ringsReferences:
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