University of GuilanJournal of Algebra and Related Topics2345-39314120160601On component extensions locally compact abelian groups1111780ENH.SahlehDepartment of Mathematics,
University of GuilanA. A.AlijaniDepartment of Mathematics,
University of Guilan0000-0002-0022-2020Journal Article20160409Let $\pounds$ 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 $\pounds$.https://jart.guilan.ac.ir/article_1780_3baf91f9c2de6e444130249948b71781.pdf