Ukrainian Mathematical Journal

, Volume 67, Issue 6, pp 975–980 | Cite as

G-Supplemented Modules

  • B. Koşar
  • C. Nebiyev
  • N. Sökmez

Following the concept of generalized small submodule, we define g -supplemented modules and characterize some fundamental properties of these modules. Moreover, the generalized radical of a module is defined and the relationship between the generalized radical and the radical of a module is investigated. Finally, the definition of amply g -supplemented modules is given with some basic properties of these modules.


Generalize Radical Direct Summand Factor Module Homomorphic Image Supplement Module 
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  1. 1.
    E. Büyükaşik and E. Türkmen, “Strongly radical supplemented modules,” Ukr. Math. J., 63, No. 8, 1140–1146 (2011).Google Scholar
  2. 2.
    J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, “Lifting modules supplements and projectivity in module theory,” Front. Math., Birkhäuser, Basel (2006).zbMATHGoogle Scholar
  3. 3.
    F. Kasch, Modules and Rings, Ludwing-Maximilian Univ., Munich (1982).zbMATHGoogle Scholar
  4. 4.
    C. Lomp, “Semilocal modules and rings,” Comm. Algebra, 1921–1935 (1999).Google Scholar
  5. 5.
    D. W. Sharpe and P. Vamos, Injective Modules, Cambridge Univ. Press (1972).Google Scholar
  6. 6.
    N. Sökmez, B. Koşar, and C. Nebiyev, “Genelleştirilmiş Küçük Alt Modüller,” XXIII Ulusal Mat. Semp., Erciyes Üniv., Kayseri (2010).Google Scholar
  7. 7.
    H. Zöschinger, “Komplementierte Moduln über Dedekindringen,” J. Algebra, 29, 42–56 (1974).Google Scholar
  8. 8.
    H. Zöschinger, “Moduln die in jeder Erweiterung ein Komplement haben,” Math. Scand., 35, 267–287 (1974).MathSciNetGoogle Scholar
  9. 9.
    H. Zöschinger, “Basis-Untermoduln und Quasi-kotorsions-Moduln über diskrete Bewertungsringen,” Bayer. Akad. Wiss. Math.-Nat. Kl. Sitzungsber, 9–16 (1977).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • B. Koşar
    • 1
  • C. Nebiyev
    • 1
  • N. Sökmez
    • 1
  1. 1.Ondokuz Mayıs UniversitySamsunTurkey

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