\begin{definition}[Definition:Divisible Abelian Group]
Let $\struct{A, +}$ be an abelian group.
Let $\struct{A, +, \circ}$ be the $\Z$-module associated with $A$.
{{explain|$A$ has been defined as a group, and then we use exactly the same letter for a module. This is suboptimal. It needs to be clarified exactly what the module is. Please use the notation and conventions that have already been established on {{ProofWiki}} in this area of mathematics. It may not be the "best", but it is what we use.
Now it should be okay by Definition:Z-Module Associated with Abelian Group/Definition 1 --Wandynsky (talk) 00:11, 31 July 2021 (UTC)}}
Then $\struct{A, +}$ is a '''divisible abelian group''' {{iff}} $\struct{A, +, \circ}$ is a divisible $\Z$-module.
Category:Definitions/Group Theory
Category:Definitions/Abelian Groups
\end{definition}