2
$\begingroup$

Let $R$ be a commutative graded ring, $m$ be its graded maximal ideal, $M$ be a finitely generated graded module over $R$.

A homogeneous ideal $I\subseteq m$ is a $M$-reduction of $m$ if $Im^{n-1}M=m^{n}M$ for some $n\in \mathbb{N}$.

Then people claimed that a homogeneous ideal $I\subseteq m$ is a $M$-reduction of $m$ if and only if $(M/IM)_{n}=0$ for $n\gg 0$.

I could not prove it. Please help me. Thanks.

  • 0
    As far as$I$know graded rings don't have only one maximal graded ideal unless they are *local. Moreover, I'm not so sure that what you say really works if $I$ can't be generated by homogeneous elements of degree $1$.2012-12-08

0 Answers 0