Some Properties of Amply Weak Essential Supplemented Modules

Öz

In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly essential supplemented module. Then every finitely M-generated module is amply weak essential supplemented. Let R be any ring. Then R is weakly essential supplemented if and only if every finitely generated R-module is amply weak essential supplemented. Let M be an amply weak essential supplemented module. Then every e-supplement submodule in M is amply weak essential supplemented.

Anahtar Kelimeler

• Essential Submodules
• Small Submodules
• Supplemented Modules
• Essential Supplemented Modules

Kaynakça

1. Birkenmeier, G. F., Mutlu, F. T., Nebiyev, C., Sökmez, N. and Tercan, A. 2010. “Goldie*-Supplemented Modules”, Glasgow Mathematical Journal, 52A, 41-52.
2. Clark, J., Lomp, C., Vanaja, N. and Wisbauer, R. (2006). “Lifting Modules: Supplements and Projectivity In Module Theory”, Frontiers in Mathematics, Birkhauser, Basel.
3. Lomp, C. 1999. “On Semilocal Modules and Rings”, Communications in Algebra, 27(4), 1921-1935.
4. Nebiyev, C. 2005. “Amply Weak Supplemented Modules”, International Journal of Computational Cognition, 3(1), 88-90.
5. Nebiyev, C. 2016a. “E-Supplemented Modules”, Antalya Algebra Days XVII, Şirince-İzmir-Türkiye.
6. Nebiyev, C. 2016b. “Weakly E-Supplemented Modules”, VII International Joint Conference of Georgian Mathematical Union & Georgian Mechanical Union, Batumi Shota Rustaveli State University, Batumi-Georgia.
7. Nebiyev, C. 2017. “Amply E-Supplemented Modules”, Caucasian Mathematics Conference II, Van Yüzüncü Yıl Univesity, Van-Türkiye.
8. Nebiyev, C. and Koşar, B. 2018. “Weakly Essential Supplemented Modules”, Turkish Studies Information Technologies & Applied Sciences, 13(29), 89-94.

9. Nebiyev, C. and Ökten, H. H. 2017. “Amply Weak E-Supplemented Modules”, VIII International Conference of the Georgian Mathematical Union, Batumi Shota Rustaveli State University, Batumi-Georgia.
10. Nebiyev, C., Ökten, H. H. and Pekin, A. 2018a. “Essential Supplemented Modules”, International Journal of Pure and Applied Mathematics, 120(2), 253-257.
11. Nebiyev, C., Ökten, H. H. and Pekin, A. 2018b. “Amply Essential Supplemented Modules”, Journal of Scientific Research & Reports, 21(4), 1-4.
12. Nebiyev, C. and Pancar, A. 2003a. “On -projective Modules”, International Journal of Applied Mathematics, 12(1), 51-57.
13. Nebiyev, C. and Pancar, A.. 2003b. “On Amply Supplemented Modules”, International Journal of Applied Mathematics, 12(3), 213-220.
14. Nebiyev, C. and Pancar, A. 2013. “On Supplement Submodules”, Ukrainian Mathematical Journal, 65(7), 961-966.
15. Nebiyev, C. and Sökmez, N. 2010. “Modules Which Lie Above a Supplement Submodule”, International Journal of Computational Cognition, 8(2), 17-18.
16. Sökmez, N., Nebiyev, C. and Koşar, B. 2008. “Equivalent Submodules of Any Module”, International Conference on Ring and Module Theory, Hacettepe University, Ankara-Türkiye.
17. Wisbauer, R. (1991). “Foundations of Module and Ring Theory”, Gordon and Breach, Philadelphia.