Let M be a module. Then M is called a D11 module if any submodule of M has a supplement which is a direct summand of M. Also M is called D11 + if every direct summand of M is D11. In this paper we investigate generalizations of D11 and D11 + modules, namely δ–D11 and δ–D11 + modules. We will prove that any δ–D11 module M has a decomposition M = M1 ⊕ M2 with δ(M1) δ M1 and δ(M2) = M2.
