Definition:Graded Abelian Group

Definition

Let $\Delta$ be a set.

A graded abelian group of type $\Delta$ is a pair $\struct {G, f}$ where:

$G$ is an abelian group

$f$ is a gradation on $G$ indexed by $\Delta$, the set of degrees.

Sources

• 1974: N. Bourbaki: Algebra I ... (previous): Chapter $\text {II}$: Linear Algebra: $\S 11$ Graded modules and rings: $1$: Graded commutative groups: Definition $1$