A proper short exact sequence 0→A→B→C→0 in the category L of locally compact abelian (LCA) groups is called ∗-pure if the induced sequence 0→A[n]→B[n]→C[n]→0 is proper exact for all positive integers n. An LCA group is called ∗-pure injective in L if it has the injective property relative to all ∗-pure sequences in L. In this paper, we give a complete description of the ∗-pure injectives in L. They coincide with the injectives in L and therefore with the pure injectives in L. Dually, we determine the topologically pure projectives in L.
Loth, P. (2015). Pure Injective and *-pure Injective LCA Groups. Rend. Sem. Mat. Univ. Padova, 133, 91-102. doi:10.4171/RSMUP/133-4