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.