Algebraic endomorphisms of LCA-groups that preserve closed subgroups

The object of this paper is the classification of those algebraic (i.e. not necessarily continuous) endomorphisms of a locally compact abelian group leaving invariant all closed subgroups. In a canonical way they turn out to form again a locally compact abelian group which can be determined up to isomorphism. If the group is totally disconnected or not periodic all endomorphisms with this property are continuous and form a topological ring.