Abstract
We introduce and study the notion of wd-Rickart modules (i.e. modules M such that for every nonzero endomorphism ϕ of M, the image of ϕ contains a nonzero direct summand of M). We show that the class of rings R for which every right R-module is wd-Rickart is exactly that of right semi-artinian right V-rings. We prove that a module M is dual Baer if and only if M is wd-Rickart and M has the strong summand sum property. Several structure results for some classes of wd-Rickart modules and dual Baer modules are provided. Some relevant counterexamples are indicated.
ACKNOWLEDGMENTS
The author would like to thank the referee for valuable suggestions and comments which improved this paper.
Notes
Communicated by E. Puczylowski.