Some Properties of r-Small Submodules

Year 2022, Volume: 15 Issue: 3, 996 - 1001, 30.12.2022

Celil Nebiyev , Hasan Hüseyin Ökten

https://doi.org/10.18185/erzifbed.876557

Abstract

In this work, some properties of r-small submodules are investigated. It is proved that the finite sum of r-small submodules is r-small. It is also proved that every homomorphic image of an r-small submodule is r-small.

Keywords

Small Submodules, Maximal Submodules, Radical, Supplemented Modules

References

• Birkenmeier, G. F., Mutlu, F. T., Nebiyev, C., Sokmez, N., Tercan, A. 2010. "Goldie*-Supplemented Modules", Glasgow Mathematical Journal, 52A, 41–52.
• Clark, J., Lomp, C., Vanaja, N., Wisbauer, R. (2006). "Lifting Modules Supplements and Projectivity In Module Theory", Frontiers in Mathematics, Birkhauser, Basel.
• Nebiyev, C., Ökten, H. H. 2020. "r-Small Submodules", 3rd International E-Conference on Mathematical Advances and Applications (ICOMAA-2020), Yıldız Technical University, Istanbul-Turkey.
• Nebiyev, C., Pancar, A. 2013. "On Supplement Submodules", Ukrainian Mathematical Journal, 65(7), 1071-1078.
• Xue, W. 1996. "Characterizations of Semiperfect and Perfect Rings", Publications Matematiques, 40, 115-125.
• Wang, Y., Ding, N. 2006. "Generalized Supplemented Modules", Taiwanese Journal of Mathematics, 10(6), 1589-1601.
• Wisbauer, R. 1991. "Foundations of Module and Ring Theory", Gordon and Breach, Philadelphia.
• Zöschinger, H. 1974. "Komplementierte Moduln Über Dedekindringen", Journal of Algebra, 29, 42-56.