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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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/

[1] B. Amini, M. Ershad and H. Sharif, “Coretractable modules”, J. Aust. Math. Soc., 86 (2009), 289–304 | DOI | MR | Zbl

[2] I. Amin, Y. Ibrahim and M. Yousif, “$(C_3)$-modules”, Lg. Coll., 22 (2015), 655–670 | MR | Zbl

[3] W. Brandal, Commutative rings whose finitely generated modules decompose, Lecture Notes in Mathematics, 723, Springer-Verlag, Berlin–Heidelberg–New-York, 1979 | DOI | MR | Zbl

[4] J. H. Cozzens, “Homological properties of the ring of differential polynomials”, Bull. Amer. Math. Soc., 76 (1970), 75–79 | DOI | MR | Zbl

[5] K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, London Math. Soc. Student Texts, 16, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[6] D. Keskin Tütüncü and R. Tribak, “On dual Baer modules”, Glasgow Math. J., 52 (2010), 261–269 | DOI | MR | Zbl

[7] D. Keskin Tütüncü, B. Kalebog̃az and P. F. Smith, “Direct sums of semi-projective modules”, Coll. Mathematicum, 127 (2012), 67–81 | DOI | MR | Zbl

[8] T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999 | DOI | MR | Zbl

[9] G. Lee, S. T. Rizvi and C. Roman, “Rickart modules”, Comm. Algebra, 38 (2010), 4005–4027 | DOI | MR | Zbl

[10] G. Lee, S. T. Rizvi and C. Roman, “Dual Rickart modules”, Comm. Algebra, 39 (2011), 4036–4058 | DOI | MR | Zbl

[11] J. C. McConnel and J. C. Robson, Noncommutative Noetherian Rings, Wiley-Interscience, Chichester, 1987 | MR | Zbl

[12] S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, 147, Cambridge University Press, 1990 | MR | Zbl

[13] R. Tribak, “On weak dual Rickart modules and dual Baer modules”, Comm. Algebra, 43 (2015), 3190–3206 | DOI | MR | Zbl

[14] A. Tuganbaev, Rings Close to Regular, Mathematics and Its Applications, 545, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002 | MR | Zbl

[15] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991 | MR | Zbl