Abstract
An R-module M is called a C4-module if, whenever A
1
and A
2
are submodules of M with
and
is an R-homomorphism with
, we have
. This notion is a non-trivial generalization of both the C3-modules and the square-free modules. Furthermore, a C4-module is called pseudo-continuous if it is also a CS -module. In this paper, we give a thorough study of the C4- and the pseudo-continuous modules.