BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.57, sa.3, ss.691-707, 2020 (SCI-Expanded)
In this paper, we introduce and study the notions of weakly circle plus-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly circle plus-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module M-R is called weakly D 2 if it satisfies the condition: for every s is an element of S and s not equal 0, if there exists n is an element of N such that s(n) not equal 0 and Im(s(n)) is a direct summand of M, then Ker(sn) is a direct summand of M. The class of weakly circle plus-supplemented-modules and weakly D2 modules contains circle plus-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.