Let $R$ be a graded ring, for example with nonnegative grading such that
$$R=R_0 \oplus R_1 \oplus \dots$$
Is then $R^n= R \times \cdots \times R$ a graded ring (not with a trivial grading) ? If so, with what grading?
2026-03-27 02:02:53.1774576973
Direct Product of a Graded Ring.
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Sure. If $G$ is a monoid (in your case the natural numbers) and $R,S$ are $G$-graded rings, then $R \times S$ has the canonical $G$-grading $(R \times S)_g = \bigoplus_{a+b=g} R_a \times S_b$.