Berna KOŞAR

Cofinitely Weak e-Supplemented Modules

ISSN: 2651-544X
Başlangıç: 2018
Yayıncı: Murat TOSUN

In this work, R will denote an associative ring with unity and all module are unital left R?modules. Let M be an R-module. If every cofinite essential submodule of M has a weak supplement in M, then M is called a cofinitely weak esupplemented (or briefly cwe-supplemented) module. In this work, some properties of these modules are investigated. Every cofinitely essential supplemented module is cwe-supplemented. Every essential supplemented module is cwe-supplemented. Every weakly essential supplemented module is cwe-supplemented. Every finitely generated cwe-supplemented module is weakly essential supplemented. Every cofinitely weak supplemented module is cwe-supplemented.

Keywords:

Cofinite Submodules, Essential Submodules, Small Submodules Supplemented Modules,

PDF

___

1 R. Alizade, G. Bilhan, P. F. Smith, Modules whose Maximal Submodules have Supplements, Comm. in Algebra, 29(6) (2001), 2389-2405.
2 R. Alizade, E. Büyükas ̧ık, Cofinitely Weak Supplemented Modules, Comm. in Algebra, 31(11) (2003), 5377-5390.
3 J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules Supplements and Projectivity In Module Theory, Frontiers in Mathematics, Birkhauser, Basel, 2006.
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, Amply Cofinitely Essential Supplemented Modules, Arch. of Curr. Res. Int., 19(1) (2019), 1-4.
6 C. Nebiyev, B. Kos ̧ar, Weakly Essential Supplemented Modules, Turkish St. Inf. Tech. and Appl. Sci., 13(29) (2018), 89-94.
7 C. Nebiyev, H. H. Ökten, A. Pekin, Essential Supplemented Modules, Int. J. of Pure and Appl. Math., 120(2) (2018), 253-257.
8 C. Nebiyev, H. H. Ökten, A. Pekin, Amply Essential Supplemented Modules, J. of Sci. Res. and Reports, 21(4) (2018), 1-4.
9 R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.