Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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⊕-ESSENTIAL SUPPLEMENTED MODULES

  • Celil Nebiyev (Department of Mathematics, Ondokuz Mayis University) ;
  • Hasan Huseyin Okten (Technical Sciences Vocational School, Amasya University)
  • Received : 2024.05.25
  • Accepted : 2024.07.26
  • Published : 2024.12.20
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Abstract

In this work ⊕ - e-supplemented modules are defined and some properties of these modules are investigated. It is proved that the finite direct sum of ⊕-e-supplemented modules is also ⊕-e-supplemented. Let M be a distributive and ⊕-e-supplemented R-module. Then every factor module and homomorphic image of M are ⊕ - e-supplemented. Let M be a ⊕ - e-supplemented R-module with SSP property. Then every direct summand of M is ⊕ - e-supplemented.

Keywords

Acknowledgement

This research was in part supported by grants from Ondokuz Mayis University (Project No: PYO.EGF.1901.19.002).

References

  1. J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules Supplements and Projectivity in Module Theory, Front. Appl. Math., Birkhauser, Basel, 2006.
  2. H. Calisici and A. Pancar, ⊕-Cofinitely supplemented modules, Czech Math J 54 (2004) no. 129, 1083-1088.
  3. A. Harmanci , D. Keskin, and P. F. Smith, On ⊕-supplemented modules, Acta Math. Hung. 83 (1999) no. 1-2, 161-169.
  4. D. Keskin, P. F. Smith, and W. Xue, Rings whose modules are ⊕-supplemented, J. Algebra 218 (1999), 470-487.
  5. B. Kosar, C. Nebiyev, and N. Sokmez, g-Supplemented modules, Ukr. Math. J. 67 (2015), no.6, 861-864.
  6. B. Kosar, C. Nebiyev, and A. Pekin, A generalization of g-supplemented modules, Miskolc Math Notes 20 (2019), no. 1, 345-352.
  7. A. Idelhadj and R. Tribak, On some properties of ⊕-supplemented modules, Int. J. Math. Sci. 69 (2003), 4373-4387.
  8. S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, Cambridge Univ. Press, Cambridge, 1990.
  9. C. Nebiyev and H. H. Okten, Some Properties of ⊕ - e-Supplemented Modules, Presented in 11th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2022), 2022.
  10. C. Nebiyev, H. H. Okten, and A. Pekin, Essential supplemented modules, Int. J. Pure Appl. Math. 120 (2018), no. 2, 253-257.
  11. C. Nebiyev, H. H. Okten, and A. Pekin, Amply essential supplemented modules, Journal of Scientific Research & Reports 21 (2018), no. 4, 1-4.
  12. C. Nebiyev and A. Pancar, On supplement submodules, Ukr. Math. J. 65 (2013), no. 7, 1071-1078.
  13. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.