A study on dual square free modules

Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule of Mis fully invariant. Let M=Li∈I Mi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free for all i ∈ I and, Mi and Lj=iMj are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let M be a quasi-projective module. If End R(M) is right dual square free, then M is dual square free. In addition, if M is finitely generated, then End R(M) is right dual square free whene ver M is dual square free. We give several examples illustrating our hypotheses.