Cohen-Macaulay graded ring/Positive characteristic/Parameter/Tight closure/Degree criterion/Inclusion/Fact

Suppose that ${}R$ is a graded Cohen-Macaulay ring of positive characteristic ${}p$ and of dimension ${}d$. Let ${}f_{1},\ldots ,f_{d}$ be a homogeneous system of parameters.

Then

${}R_{\geq \operatorname {deg} (f_{1})+\cdots +\operatorname {deg} (f_{d})}\subseteq {\left(f_{1},\ldots ,f_{d}\right)}^{*}\,.$

Proof, Write another proof