Let $R$ be a domain and $A$ an $R$-module. Exercise 2.38 (ii) in Rotman's An Introduction to Homological Algebra says
Prove that if the multiplication $\mu_r \colon A \to A$ is a surjection for all $r \neq 0$, then $A$ is divisible.
Am I right in thinking that the statement is false if one interprets the question as asking about the divisibility of $A$ as an abelian group? Any field of positive characteristic (as a module over itself) seems to be a counter-example.
My confusion arises from the fact that at this point in the book, divisibility has only been defined for abelian groups and not $R$-modules.