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On generalization of ⊕-cofinitely supplemented modules

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Ukrainian Mathematical Journal Aims and scope

We study the properties of ⊕-cofinitely radical supplemented modules, or, briefly, cgs ⊕-modules. It is shown that a module with summand sum property (SSP) is cgs ⊕ if and only if M/w Loc⊕ M (w Loc⊕ M is the sum of all w-local direct summands of a module M) does not contain any maximal submodule, that every cofinite direct summand of a UC-extending cgs ⊕-module is cgs ⊕, and that, for any ring R, every free R-module is cgs ⊕ if and only if R is semiperfect.

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References

  1. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991).

    MATH  Google Scholar 

  2. R. Alizade, G. Bilhan, and P. F. Smith, “Modules whose maximal submodules have supplements,” Commun. Algebra, 29, No. 6, 2389–2405 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Harmancı, D. Keskin, and P. F. Smith, “On ⊕-supplemented modules,” Acta Math. Hungar., 83, No. 1–2, 161–169 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Çalışıcı and A. Pancar, “⊕-Cofinitely supplemented modules,” Czech. Math. J., 54, No. 129, 1083–1088 (2004).

    MATH  Google Scholar 

  5. J. Clark, C. Lomp, N. Vajana, and R. Wisbauer, Lifting Modules, Birkhäuser, Basel (2006).

    MATH  Google Scholar 

  6. Y. Wang and N. Ding, “Generalized supplemented modules,” Taiwan. J. Math., 10, No. 6, 1589–1601 (2006).

    MATH  MathSciNet  Google Scholar 

  7. E. Büyükaşık and C. Lomp, “On a recent generalization of semiperfect rings,” Bull. Austral. Math. Soc., 78, 317–325 (2008).

    Article  MATH  Google Scholar 

  8. M. T. Koşan, “Generalized cofinitely semiperfect modules,” Int. Electron. J. Algebra, 5, 58–69 (2009).

    MATH  MathSciNet  Google Scholar 

  9. A. Ç. Özcan, A. Harmancı, and P. F. Smith, “Duo modules,” Glasgow Math. J. Trust., 48, 533–545 (2006).

    Article  MATH  Google Scholar 

  10. A. Idelhadj and R. Tribak, “On some properties of ⊕-supplemented modules,” Int. J. Math. Math. Sci., 69, 4373–4387 (2003).

    Article  MathSciNet  Google Scholar 

  11. S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, Cambridge University Press, Cambridge (1990).

    Book  MATH  Google Scholar 

  12. G. Puninski, “Projective modules over the endomorphism ring of a biuniform module,” J. Pure Appl. Algebra, 188, 227–246 (2004).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Ondokuz Mayıs University, Samsun, Turkey

    B. Nisanci & A. Pancar

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  1. B. Nisanci
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  2. A. Pancar
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 183–189, February, 2010.

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Nisanci, B., Pancar, A. On generalization of ⊕-cofinitely supplemented modules. Ukr Math J 62, 203–209 (2010). https://doi.org/10.1007/s11253-010-0344-4

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  • DOI: https://doi.org/10.1007/s11253-010-0344-4

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