Let M = Ln i=1 Mi be a flnite direct sum of modules. We prove: (i) If Mi is radical Mj-projective for all j > i and each Mi is H-supplemented, then M is H-supplemented. (ii) If all the Mi are relatively projective and M is H-supplemented, then each Mi is H-supplemented. Let ‰ be the preradical for a cohereditary torsion theory. Let M be a module such that ‰(M) has a unique coclosure and every direct summand of ‰(M) has a coclosure in M. Then M is H-supplemented if and only if there exists a decomposition M = M1 ' M2 such that M2 ⊆ ‰(M), ‰(M)=M2 ¿ M=M2, and M1; M2 are H-supplemented.
