Resumen

Let T be a hereditary torsion theory on the module category R-Mod and let A be a module. A module D is called A-T-divisible if for every T-closed (T-saturated) submodule B of A, every homomorphism B-->D extends to a homomorphism A-->D. The notions of T-divisible and self-T-divisible module are those naturally deduced from the above definition. We discuss connections between, on the one hand, (self-)T-divisible modules and, on the other hand, T-complemented and self-c-injective modules. We show that a finite direct sum of relatively injective modules is self-T-divisible if and only if each direct summand is self-T-divisible.