Question

Use Proposition 3.12, Corollary 19.15, and Exercise 19.8 to show that if $R=k\left[x_0, \ldots, x_n\right] / I$ is a graded ring, then $R$ is CohenMacaulay iff $R_P$ is Cohen-Macaulay, where $P=\left(x_0, \ldots, x_n\right)$.

   Use Proposition 3.12, Corollary 19.15, and Exercise 19.8 to show that if $R=k\left[x_0, \ldots, x_n\right] / I$ is a graded ring, then $R$ is CohenMacaulay iff $R_P$ is Cohen-Macaulay, where $P=\left(x_0, \ldots, x_n\right)$.

Commutative Algebra: with a View Toward Algebraic Geometry

David Eisenbud 1st Edition

Chapter 19, Problem 10

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Use Proposition 3.12, Corollary 19.15, and Exercise 19.8 to show that if $R=k\left[x_0, \ldots, x_n\right] / I$ is a graded ring, then $R$ is CohenMacaulay iff $R_P$ is Cohen-Macaulay, where $P=\left(x_0, \ldots, x_n\right)$.

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