Coefficient ideals and the Cohen-Macaulay property of Rees algebras

Hyry, Eero

doi:10.1090/S0002-9939-00-05673-2

Coefficient ideals and the Cohen-Macaulay property of Rees algebras
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Proc. Amer. Math. Soc. 129 (2001), 1299-1308 Request permission

Abstract:

Let $A$ be a local ring and let $I\subset A$ be an ideal of positive height. If $J\subset I$ is a reduction of $I$, then the coefficient ideal $\mathfrak {a}(I,J)$ is by definition the largest ideal $\mathfrak {a}$ such that $I\mathfrak {a}= J\mathfrak {a}$. In this article we study the ideal $\mathfrak {a}(I,J)$ when the Rees algebra $R_A(I)$ is Cohen-Macaulay.

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