s-pure extensions of locally compact abelian groups

Abstract

A subgroup H of a locally compact abelian (LCA) group G is called s-pure if H 􏰂 nG = H for every positive integer n. A proper short exact sequence 0→A→φ B→C→0 in the category of LCA groups is said to be s-pure if φ(A) is an s-pure subgroup of G. We establish conditions under which the s-pure exact sequences split and determine those LCA groups which are s-pure injective. We also gives a necessary condition for an LCA group to be s-pure projective in £.