Recall a module M is said to be d-Rickart if for every endomorphism of M, Im is a direct summand of M. also a module M is called retractable if, for every nonzero submodule N M, there exists a nonzero endomorphism of M such that Im N. It was shown that if M is a retractable d-Rickart module, then every nonzero submodule contains a nonzero direct summand of M. We introduce the notion of Wd-Rickart modules; i.e. modules M such that for every nonzero endomorphism of M, Im contains a nonzero direct summand of M.
