Self-pure-generators over Dedekind domains

Abstract

We prove that all pure submodules of a finite rank torsion-free module $A$ over a Dedekind domain are $A$-generated if and only if $A$ has a rank $1$ direct summand $B$ such that $\mathbf{type}(B)$ is the inner type of $A$.

V2: major revision. A new section about direct products of tffr groups is added