C 4-Modules.

AnR-moduleM is called aC4-module if, wheneverA1andA2are submodules ofMwithandis anR-homomorphism with, we have. This notion is a non-trivial generalization of both theC3-modules and the square-free modules. Furthermore, aC4-module is called pseudo-continuous if it is also aCS-module. In this paper, we give a thorough study of theC4- and the pseudo-continuous modules. [ABSTRACT FROM AUTHOR]