On (Completely) Weak* Rad-\(\oplus \)-Supplemented Modules

  • Manoj Kumar PatelEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 228)


In this paper, we establish various properties of weak* Rad-\(\oplus \)-supplemented modules and completely weak* Rad-\(\oplus \)-supplemented modules, which are the generalizations of \(\oplus \)–supplemented and Rad-\(\oplus \)-supplemented modules. Our main focus is to characterize the weak* Rad-\(\oplus \)-supplemented modules in terms of radical modules, modules having property \((p^*)\) and w–local modules.


Rad-\(\oplus \)-supplemented module Weak* Rad-\(\oplus \)-supplemented module Completely weak* Rad-\(\oplus \)-supplemented module 


  1. 1.
    Al-Khazzi, I., Smith, P.F.: Modules with chain conditions on superfluous submodules. Comm. Alg. 19, 2331–2351 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buyukasik, E., Mermut, E., Ozdemir, S.: Rad-supplemented modules. Rend. Sem. Mat. Univ. Padova. 124, 157–177 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cahsici, H., Turkmen, E.: Generalized \(\oplus \)–supplemented modules. Alg. Dis. Math. 10, 10–18 (2010)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Choubey, S.K., Patel, M.K., Kumar, V.: On weak* Rad-\(\oplus \)-supplemented modules. Maejo Int. J. Sci. Tech. 11(03), 264–274 (2017)Google Scholar
  5. 5.
    Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.: Lifting Modules. Frontiers in Mathematics, 1st edn. Birkhaeuser Basel, Boston (2006)Google Scholar
  6. 6.
    Kasch, F.: Modules and Rings. Academic Press Inc., London (1982)Google Scholar
  7. 7.
    Patel, M.K., Pandeya, B.M., Kumar, V.: Generalization of semi-projective modules. Int. J. Comp. Appl. 83, 1–6 (2013)Google Scholar
  8. 8.
    Wisbauer, R.: Foundations of Modules and Rings Theory, 1st edn. Gordon and Breach Sci. Pub. (1991)Google Scholar
  9. 9.
    Xue, W.: Characterizations of semiperfect and perfect rings. Pub. Matematiq. 40, 115–125 (1996)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology NagalandDimapurIndia

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