Cofinitely eg-Supplemented Modules

Year 2020, Volume: 3 Issue: 1, 77 - 81, 15.12.2020

Celil Nebiyev , Hasan Hüseyin Ökten

Abstract

Let M be an R-module. If every cofinite essential submodule of M has a g-supplement in M, then M is called a cofinitely essential g-supplemented (or briefly cofinitely eg-supplemented) module. In this work, some properties of these modules are investigated.

Keywords

Cofinite Submodules, Essential Submodules, g-Small Submodules, g-Supplemented Modules

References

• 1 R. Alizade, G. Bilhan, P. F. Smith, Modules whose Maximal Submodules have Supplements, Comm. in Algebra 29(6) (2001), 2389-2405.
• 2 J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules Supplements and Projectivity In Module Theory, Frontiers in Mathematics, Birkhauser, Basel, 2006.
• 3 B. Koşar, Cofinitely g-Supplemented Modules, British J. of Math. and Comp. Sci., 14(4) (2016), 1-6.
• 4 B. Koşar, C. Nebiyev, Cofinitely Essential Supplemented Modules, Turkish St. Inf. Tech. and Appl. Sci., 13(29) (2018), 83-88.
• 5 B. Koşar, C. Nebiyev, N. Sökmez, g-Supplemented Modules, Ukrainian Math. J., 67(6) (2015), 861-864.
• 6 B. Koşar, C. Nebiyev, A. Pekin, A Generalization of g-Supplemented Modules, Miskolc Math. Notes, 20(1) (2019), 345-352.
• 7 C. Nebiyev, H. H. Ökten, Essential g-Supplemented Modules, Turkish St. Inf. Tech. and Appl. Sci., 14(1) (2019), 83-89.
• 8 C. Nebiyev, On a Generalization of Supplement Submodules, Int. J. of Pure and Appl. Math. 113 (2) (2017), 283-289.
• 9 C. Nebiyev, H. H. Ökten, A. Pekin, Essential Supplemented Modules, Int. J. of Pure and Appl. Math., 120(2) (2018), 253-257.
• 10 R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.