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http://dx.doi.org/10.4134/BKMS.b190420

WEAKLY ⊕-SUPPLEMENTED MODULES AND WEAKLY D2 MODULES  

Hai, Phan The (Department for Management of Science and Technology Development Ton Duc Thang University)
Kosan, Muhammet Tamer (Department of Mathematics Gazi University)
Quynh, Truong Cong (The University of Danang - University of Science and Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.3, 2020 , pp. 691-707 More about this Journal
Abstract
In this paper, we introduce and study the notions of weakly ⊕-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly ⊕-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module MR is called weakly D2 if it satisfies the condition: for every s ∈ S and s ≠ 0, if there exists n ∈ ℕ such that sn ≠ 0 and Im(sn) is a direct summand of M, then Ker(sn) is a direct summand of M. The class of weakly ⊕-supplemented-modules and weakly D2 modules contains ⊕-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.
Keywords
(weakly) ${\oplus}$-supplemented module; (weakly) D2 module; GD2 module; supplement submodule; semiperfect ring; projective cover;
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