s-pure extensions of locally compact abelian groups

Year 2015, Volume: 44 Issue: 5, 1125 - 1132, 01.10.2015

H. Sahleh A.a. Alijani

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 £.

Keywords

s-pure injective, s-pure projective, s-pure extension

References

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