Definition:Divisible Abelian Group

Definition

Let $\struct{A, +}$ be an abelian group.

Let $\struct{A, +, \circ}$ be the $\Z$-module associated with $A$.

This article, or a section of it, needs explaining. In particular: $A$ 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 $\mathsf{Pr} \infty \mathsf{fWiki}$ 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) You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

Then $\struct{A, +}$ is a divisible abelian group if and only if $\struct{A, +, \circ}$ is a divisible $\Z$-module.