JournalsrsmupVol. 133pp. 91–102

Pure injective and \ast-pure injective LCA groups

  • Peter Loth

    Sacred Heart University, Fairfield, USA
Pure injective and $\ast$-pure injective LCA groups cover
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Abstract

A proper short exact sequence 0ABC00\to A\to B\to C\to 0 in the category L\mathcal L of locally compact abelian (LCA) groups is called \ast-pure if the induced sequence 0A[n]B[n]C[n]00\to A[n]\to B[n]\to C[n]\to 0 is proper exact for all positive integers nn. An LCA group is called \ast-pure injective in L\mathcal L if it has the injective property relative to all \ast-pure sequences in L\mathcal L. In this paper, we give a complete description of the \ast-pure injectives in L\mathcal L. They coincide with the injectives in L\mathcal L and therefore with the pure injectives in L\mathcal L. Dually, we determine the topologically pure projectives in L\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