Pure injective and -pure injective LCA groups

  • Peter Loth

    Sacred Heart University, Fairfield, USA

Abstract

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

Cite this article

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

DOI 10.4171/RSMUP/133-4