Generating an injective class of torsion-free Abelian groups
Let \(\Lambda\) be a set of torsionfree abelian groups of finite rank. The class \({\mathcal C}^ 0(\Lambda)\) consists of those torsionfree finite rank groups C such that each \(A\in \Lambda\) is injective with respect to any pure exact sequence E: \(0\to B\to C\to K\to 0\). Further, \({\mathcal I}{\mathcal C}^ 0(\Lambda)\) denotes the class of all torsionfree finite rank groups which are injective with respect to all pure exact sequences E with C from \({\mathcal C}^ 0(\Lambda)\). The author characterizes the classes \({\mathcal C}^ 0(\Lambda)\) and \({\mathcal I}{\mathcal C}^ 0(\Lambda)\) in the case when \(\Lambda\) consists of torsionfree groups of rank one. In the last part the dual (projective) case is considered.
torsionfree abelian groups of finite rank
scientific article; zbMATH DE number 4114891