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Original Articles

Weak Rickart and dual weak Rickart objects in abelian categories

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Pages 2912-2926 | Received 01 Mar 2017, Published online: 15 Dec 2017

References

  • Albu, T., Iosif, M. (2015). Lattice preradicals with applications to Grothendieck categories and torsion theories. J. Algebra 444:339–366.
  • Anderson, F. W., Fuller, K. R. (1992). Rings and Categories of Modules. New York: Springer.
  • Clark, J., Lomp, C., Vanaja, N., Wisbauer, R. (2006). Lifting Modules, Frontiers in Mathematics. Basel, Boston, Berlin: Birkhauser Verlag.
  • Crivei, S., Kör, A. (2016). Rickart and dual Rickart objects in abelian categories. Appl. Categor. Struct. 24:797–824.
  • Cuadra, J., Simson, D. (2007). Flat comodules and perfect coalgebras. Commun. Algebra 35:3164–3194.
  • Dăscălescu, S., Năstăsescu, C., Raianu, C. (2001). Hopf Algebras. An Introduction. New York: Marcel Dekker.
  • Dăscălescu, S., Năstăsescu, C., Tudorache, A. (2011). A note on regular objects in Grothendieck categories. Arab. J. Sci. Eng. 36:957–962.
  • Dăscălescu, S., Năstăsescu, C., Tudorache, A., Dăuş, L. (2006). Relative regular objects in categories. Appl. Categor. Struct. 14:567–577.
  • Dăuş, L. (2011). Relative regular modules. Applications to von Neumann regular rings. Appl. Categor. Struct. 19: 859–863.
  • Dăuş, L., Năstăsescu, C., Van Oystaeyen, F. (2009). V-categories: Applications to graded rings. Commun. Algebra 37:3248–3258.
  • Dung, N. V., Huynh, N. V., SmithP. F, ., Wisbauer, R. (1994). Extending modules, Pitman Research Notes, Vol. 313, Longman Scientific and Technical.
  • Dung, N. V., Smith, P. F. (1992). On semi-artinian V-modules. J. Pure Appl. Algebra 82:27–37.
  • Haily, A., Rahnaoui, H. (2011). Baer and quasi-Baer modules over some classes of modules. Kyungpook Math. J. 51:375–384.
  • Keskin Tütüncü, D., Tribak, R. (2010). On dual Baer modules. Glasgow Math. J. 52:261–269.
  • Keskin Tütüncü, D., Tribak, R. (2009). On 𝒯-noncosingular modules. Bull. Aust. Math. Soc. 80:462–471.
  • Lam, T. Y. (1998). Lectures on Modules and Rings, Graduate Texts in Mathematics, Vol. 189. New York: Springer.
  • Lee, G., Rizvi, S. T., Roman, C. (2010). Rickart modules. Commun. Algebra 38:4005–4027.
  • Lee, G., Rizvi, S. T., Roman, C. (2011). Dual Rickart modules. Commun. Algebra 39:4036–4058.
  • Lee, G., Rizvi, S. T., Roman, C. (2012). Direct sums of Rickart modules. J. Algebra 353:62–78.
  • Mitchell, B. (1965). Theory of Categories. New York: Academic Press.
  • Mohamed, S. H., Müller, B. J. (1990). Continuous and Discrete Modules, London Mathematical Society Lecture Notes Series, Vol. 147. Cambridge, New York: Cambridge University Press.
  • Năstăsescu, C., Van Oystaeyen, F. (1987). Dimensions of Ring Theory. Dordrecht: D. Reidel Publishing Company.
  • Nicholson, W. K., Zhou, Y. (2006). Semiregular morphisms. Commun. Algebra 34:219–233.
  • Rizvi, S. T., Roman, C. (2004). Baer and quasi-Baer modules. Commun. Algebra 32:103–123.
  • Rizvi, S. T., Roman, C. S. (2007). On 𝒦-nonsingular modules and applications. Commun. Algebra 35:1–22.
  • Stenstöm, B. (1975). Rings of Quotions, Grundlehren der Math., Vol. 27. Berlin: Springer.
  • Tribak, R. (2015). On weak dual Rickart modules and dual Baer modules. Commun. Algebra 43:3190–3206.
  • Wang, M. (2001). Some studies on QcF-coalgebras. In International Symposium on Ring Theory (Kyongju, 1999), Trends Math. Boston: Birkhäuser, pp. 393–399.
  • Wisbauer, R. (1991). Foundations of Module and Ring Theory. Reading: Gordon and Breach.

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