C4-Modules. Issue 4 (3rd April 2017) - Ding, Nanqing; Ibrahim, Yasser; Yousif, Mohamed; Zhou, Yiqiang
ABSTRACT: An R -module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with M = A 1 ⊕ A 2 and f : A 1 → A 2 is an R -homomorphism with ker f ⊆ ⊕ A 1, we have I m f ⊆ ⊕ A 2 . This notion is a non-trivial generalization of both the C 3-modules and the square-free modules. Furthermore, a C 4-module is called pseudo-continuous if it is also a CS -module. In this paper, we give a thorough study of the C 4- and the pseudo-continuous modules.