Note on ideal-transforms, Rees rings, and Krull rings (Q1094459)
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scientific article; zbMATH DE number 4025554
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on ideal-transforms, Rees rings, and Krull rings |
scientific article; zbMATH DE number 4025554 |
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Note on ideal-transforms, Rees rings, and Krull rings (English)
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1987
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The main result gives several necessary and sufficient conditions for the ideal transform T(I) to be finitely generated over R, when I is a height one ideal in an important class of two-dimensional local rings R. One of these conditions is that the integral closure of T(I) coincides with the complete integral closure of T(I). Then it is shown that if I is an ideal in a Noetherian ring and I contains a regular element, then the complete integral closure of T(I) is always a Krull ring. This is applied to certain symbolic Rees rings.
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ideal transform
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complete integral closure
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Krull ring
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symbolic Rees rings
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