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In this text, the notion of mutually ss-supplemented modules characterizes with the help of semiperfect rings. For this mutually ss-supplemented modules were first classified according to certain properties. These features can be listed as follows in the refinable modules, distributive modules, fully invariant submodules and (π-) projective modules. Especially it was proven that each 𝜋-projective mutually ss-supplemented module is amply mutually ss-supplemented. It was obtained that every ss-supplemented refinable module has direct summand which is a mutually ss-supplement in the module. It was shown that C=⨁_ (ϱ∈Λ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules C_ϱ _ (ϱ∈Λ).
Türkmen et al. (Wed,) studied this question.