Quasi Cancellation R-Modules

Let r be a commutative ring with identity, and let m be a unitary left r-module. in this work, we introduce quasi cancellation r-module (weakly quasi cancellation r-module) concept as a generalization of cancellation r-module (weakly cancellation r-module) concept we generalize some properties of cancellation (weakly cancellation) r-modules to quasi cancellation (weakly quasi cancellation) r-modules. furthermore, we give some conditions under which r-module m is quasi cancellation r-module.