### Peter Loth

Sacred Heart University, Fairfield, USA

## Abstract

A proper short exact sequence $0\to A\to B\to C\to 0$ in the category $\mathcal L$ of locally compact abelian (LCA) groups is called *$\ast$-pure* if the induced sequence $0\to A[n]\to B[n]\to C[n]\to 0$ is proper exact for all positive integers $n$. An LCA group is called *$\ast$-pure injective in $\mathcal L$* if it has the injective property relative to all $\ast$-pure sequences in $\mathcal L$. In this paper, we give a complete description of the $\ast$-pure injectives in $\mathcal L$. They coincide with the injectives in $\mathcal L$ and therefore with the pure injectives in $\mathcal L$. Dually, we determine the topologically pure projectives in $\mathcal L$.

## Cite this article

Peter Loth, Pure injective and $\ast$-pure injective LCA groups. Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 91–102

DOI 10.4171/RSMUP/133-4