I don't have my hands on the book of Nastasescu and Van Oystaeyen on graded rings, which I believe contains this result, but here is a reference to a paper by H. Huishi Li, "On Monoid Graded Local Rings", where the author proves, in section 2, that in a $\Gamma$-graded ring, $A$, where $A=\bigoplus_{\gamma\in\Gamma}A_{\gamma},$$where$\Gamma$is a cancellation monoid with neutral element$e$, one has that$A_e$is a local ring if and only if the graded two-sided ideal generated by homogeneous non-units is proper. 1 I don't have my hands on the book of Nastasescu and Van Oystaeyen on graded rings, which I believe contains this result, but here is a reference to a paper by H. Li, "On Monoid Graded Local Rings", where the author proves, in section 2, that in a$\Gamma$-graded ring,$A$, where$\Gamma$is a cancellation monoid with neutral element$e$, one has that$A_e\$ is a local ring if and only if the graded two-sided ideal generated by homogeneous non-units is proper.