Definition

Let $G$ be an abelian group.

Let $\Delta$ be a set.

A gradation of type $\Delta$ on $G$ is a family of subgroups $\family {G_\lambda}_{\lambda \in \Delta}$ of which $G$ is the internal direct sum.

Sources

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