On Weak Dual Rickart Modules and Dual Baer Modules

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.

Key Words:

• Dual Rickart modules
• Dual Baer modules
• Endomorphism rings
• Semipotent rings and modules
• Weak dual Rickart modules

2010 Mathematics Subject Classification:

• 16D10
• 16D70
• 16S50
• 16D80

ACKNOWLEDGMENTS

The author would like to thank the referee for valuable suggestions and comments which improved this paper.

Notes

Communicated by E. Puczylowski.