Question

(A. Micali). Let $(R, m)$ be a Noetherian local ring. Show that $m$ is of linear type if and only if $R$ is a regular local ring.

   (A. Micali). Let $(R, m)$ be a Noetherian local ring. Show that $m$ is of linear type if and only if $R$ is a regular local ring.

Integral Closure: Rees Algebras, Multiplicities, Algorithms

Integral Closure: Rees Algebras, Multiplicities, Algorithms

Wolmer Vasconcelos 1st Edition

Chapter 1, Problem 5

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A Noetherian local ring $(R,m)$ has a unique maximal ideal $m$. An ideal $I$ is said to be of linear type if the symmetric algebra $S_R(I)$ is isomorphic to the Rees algebra $R[It]$. A regular local ring is a Noetherian local ring whose maximal ideal can be Show more…

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(A. Micali). Let $(R, m)$ be a Noetherian local ring. Show that $m$ is of linear type if and only if $R$ is a regular local ring.

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