Finitely Essential Supplemented Modules

Abstract

In this work, finitely essential supplemented modules are defined and some properties of these modules are investigated. Let M be a finitely essential supplemented module. If M is noetherian, then M is essential supplemented.

Keywords

• Small Submodules
• Radical
• Essential Submodules
• Supplemented Modules

References

1. G. F. Birkenmeier, F. T. Mutlu, C. Nebiyev, N. Sokmez and A. Tercan, Goldie*-Supplemented Modules, Glasgow Mathematical Journal, 52A, 41–52 (2010).
2. J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules Supplements and Projectivity In Module Theory, Frontiers in Mathematics, Birkhauser, Basel, 2006.
3. C. Nebiyev and H. H. Ökten, Finitely e-Supplemented Modules, Presented in 9th International Eurasian Conference on Mathematical Sciences and Applications, Scopje-North Macedonia, (2020).
4. C. Nebiyev, H. H. Ökten and A. Pekin, Essential Supplemented Modules, International Journal of Pure and Applied Mathematics, 120 No.2, 253-257 (2018).
5. C. Nebiyev, H. H. Ökten and A. Pekin, Amply Essential Supplemented Modules, Journal of Scientific Research and Reports, 21 No.4, 1-4 (2018).
6. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.
7. H. Zöschinger, Komplementierte Moduln Über Dedekindringen, Journal of Algebra, 29, 42-56 (1974).