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Siberian Mathematical Journal

, Volume 46, Issue 2, pp 359–363 | Cite as

Cofinitely semiperfect modules

  • H. Calisici
  • A. Pancar
Article

Abstract

It is well known that a projective module M is ⊕-supplemented if and only if M is semiperfect. We show that a projective module M is ⊕-cofinitely supplemented if and only if M is cofinitely semiperfect or briefly cof-semiperfect (i.e., each finitely generated factor module of M has a projective cover). In this paper we give various properties of the cof-semiperfect modules. If a projective module M is semiperfect then every M-generated module is cof-semiperfect. A ring R is semiperfect if and only if every free R-module is cof-semiperfect.

Keywords

semiperfect ring cofinitely submodule cofinitely semiperfect module 

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References

  1. 1.
    Çalışıcı H. and Pancar A., “⊕-cofinitely supplemented modules,” Czech. Math. J., 54, No.129, 1083–1088 (2004).CrossRefGoogle Scholar
  2. 2.
    Wisbauer R., Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991).Google Scholar
  3. 3.
    Mohamed S. H. and Müller B. J., Continuous and Discrete Modules, Cambridge Univ. Press, Cambridge (1990). (London Math. Soc.; LNS 147.)Google Scholar
  4. 4.
    Alizade R., Bilhan G., and Smith P. F., “Modules whose maximal submodules have supplements,” Comm. Algebra, 29, No.6, 2389–2405 (2001).CrossRefGoogle Scholar
  5. 5.
    Keskin D., Smith P. F., and Xue W., “Rings whose modules are ⊕-supplemented,” J. Algebra, 218, 470–487 (1999).CrossRefGoogle Scholar
  6. 6.
    Harmancı A., Keskin D., and Smith P. F., “On ⊕-supplemented modules,” Acta Math. Hungar., 83, 161–169 (1999).CrossRefGoogle Scholar
  7. 7.
    Kasch F., Modules and Rings, Acad. Press, London (1982).Google Scholar
  8. 8.
    Garcia J. L., “Properties of direct summands of modules,” Comm. Algebra, 17, 73–92 (1989).Google Scholar
  9. 9.
    Lomp C., “On semilocal modules and rings,” Comm. Algebra, 27, 1921–1935 (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • H. Calisici
    • 1
  • A. Pancar
    • 2
  1. 1.Ondokuz Mayis UniversityAmasyaTurkey
  2. 2.Ondokuz Mayis UniversitySamsunTurkey

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