Reduction numbers and Rees algebras of powers of an ideal

Hoa, Lê Tuan

doi:10.1090/S0002-9939-1993-1152984-0

Reduction numbers and Rees algebras of powers of an ideal
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Proc. Amer. Math. Soc. 119 (1993), 415-422 Request permission

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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