On component extensions locally compact abelian groups

Let \pounds be the category of locally compact abelian groups and A,C\in \pounds. In this paper, we define component extensions of A by C and show that the set of all component extensions of A by C forms a subgroup of Ext(C,A) whenever A is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. We also gives a necessary condition for an LCA group to be component injective in \pounds.

Keywords:

Component extension , component injective , component projective