### On dual Rickart modules and weak dual Rickart modules

#### Abstract

Let \(R\) be a ring. A right \(R\)-module \(M\) is called \(\mathrm{d}\)-

*Rickart*if for every endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) is a direct summand of \(M\) and it is called \(\mathrm{wd}\)-*Rickart*if for every nonzero endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) contains a nonzero direct summand of \(M\). We begin with some basic properties of \(\mathrm{(w)d}\)-Rickart modules. Then we study direct sums of \(\mathrm{(w)d}\)-Rickart modules and the class of rings for which every finitely generated module is \(\mathrm{(w)d}\)-Rickart. We conclude by some structure results.#### Keywords

dual Rickart modules, weak dual Rickart modules, weak Rickart rings, V-rings

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