In Theorem 3.1 of Graded rings over arithmetical orders, the authors prove that for a strongly $\mathbb{Z}$-graded ring $R$, if $R_0$ is left and right Goldie and a maximal order in its (classical) quotient ring $Q_0$, then $R$ is a maximal order in its quotient ring $Q$. Here strongly graded means that if $R = \oplus_{i\in\mathbb{Z}}R_i$, then $R_iR_j= R_{i+j}$, rather than merely graded rings which satisfy $R_iR_j\subset R_{i+j}$. My question is: is this still the case when the grading is taken modulo an integer? i.e. when $R$ is a strongly $\mathbb{Z}/n\mathbb{Z}$-graded ring, so $R_iR_j= R_{i+j\bmod n}$, does $R_0$ left and right Goldie, and a maximal order, imply $R$ is a maximal order?



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