Geodesic
On dual Rickart modules and weak dual Rickart modules
Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 200-214

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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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     author = {Derya Keskin T\"ut\"unc\"u and Nil Orhan Erta\c{s} and Rachid Tribak},
     title = {On dual {Rickart} modules and weak dual {Rickart} modules},
     journal = {Algebra and discrete mathematics},
     pages = {200--214},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a3/}
}
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Derya Keskin Tütüncü; Nil Orhan Ertaş; Rachid Tribak. On dual Rickart modules and weak dual Rickart modules. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 200-214. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a3/