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