Let $M$ be a finitely generated graded $A$-module with $\dim M=0.$ Let $M$ be $\mathbb Z$-graded and $A$ be $\mathbb N$-graded Noetherian ring. Then how can we say that the Hilbert function of $M$ is polynomial equivalent to a constant polynomial ?
What I know that under these condition $l_A(M)< \infty.$
Help me. Thanks.