Definition:Z-Graded Ring

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Definition

Let $\Z$ be the set of integers.


A $\Z$-graded ring is a graded ring of type the additive group of integers.

That is, it is a pair $\struct {R, f}$ where:

$R$ is a ring
$f$ is a family $\family {R_n}_{n \mathop \in \Z}$ of subgroups of the additive group of $R$, of which it is the internal direct sum, and such that:
$\forall x \in R_n, y \in R_m: x y \in R_{m + n}$


Also see


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