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