Definition:Gradation on Abelian Group

Definition
Let $G$ be an abelian group.

Let $\Delta$ be a set.

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

Also see

 * Definition:Graded Abelian Group