Let $A$ be a $\mathbb{Z}_{\geq 0}$-graded ring, $f \in A$ - homogenious, and $I \subset A$ - homogenious ideal. Let $A_f$ be its localization, and $A_{(f)}$ - subring of elements of degree 0. How to show, that
$ (A/I)_{(f)} = A_{(f)}/(I A_f \cap A_{(f)})? $
It is used in Hartshorne, Algebraic geometry, section 1.3, proposition 3.4