Algebraically compact abelian $TI$-groups

An abelian group $G$ is called a $TI$-group if every associative ring with additive group $G$ is filial. An abelian group $G$ such that every (associative) ring with additive group $G$ is an $SI$-ring (a hamiltonian ring) is called an $SI$-group (an $SI_H$-group). In this paper, $TI$-groups, as well as $SI$-groups and $SI_H$-groups are described in the class of reduced algebraically compact abelian groups.