(untitled) (European Journal of Pure and Applied Mathematics, 2012)
LetÂ M and X be R-modules. We define the X–supplementedÂ modules via the class Â B(M,X) as a generalization of -supplementedÂ modules. We show that any finite direct sum ofÂ X–supplementedÂ modules isÂ X–supplemented. It is given a number of necessary andÂ sufficient conditions for every direct summand of an Â X–supplementedÂ module to beÂ X–supplemented.