Abstract Let R be a ring and let M be an R-module with S = EndR(M). The module M is called quasi-dual Baer if for every fully invariant submodule N of M, {φ ∈ S | Imφ ⊆ N} = eS for some idempotent e in S. We show that M is quasi-dual Baer if and only if ϕ∈I ϕ(M) is a direct summand of M for every left ideal I of S. The R-module RR is quasi-dual Baer if and only if R is a finite product of simple rings. Other characterizations of quasi-dual Baer modules are obtained. Examples which delineate the concepts and results are provided.
