Document Type

Article

Publication Date

2015

Abstract

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.


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Algebra Commons

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