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Reduction numbers and Rees algebras of powers of an ideal


Author: Lê Tuan Hoa
Journal: Proc. Amer. Math. Soc. 119 (1993), 415-422
MSC: Primary 13A30; Secondary 13D45, 13H10
DOI: https://doi.org/10.1090/S0002-9939-1993-1152984-0
MathSciNet review: 1152984
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Abstract: Let $ I$ be an ideal in a Noetherian local ring $ (R,\mathfrak{m})$. It is shown that for $ n \gg 0$ the reduction number $ {r_J}({I^n})$ of $ {I^n}$ with respect to a minimal reduction $ J$ is not only independent from the choice of $ J$ but also is stable. If $ I$ is an $ \mathfrak{m}$-primary ideal, we give a criterion for the Rees algebra $ R[{I^n}t]$ with $ n \gg 0$ to be Cohen-Macaulay.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152984-0
Keywords: Minimal reduction, reduction number, associated graded ring, Rees algebra, Cohen-Macaulay ring
Article copyright: © Copyright 1993 American Mathematical Society

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