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  £ .