Cancellation and Weak Cancellation S-Acts

Abstract

The purpose of this work is to introduce and study a generalization of the cancellation (weak cancellation) of modules to acts. Then some notions related of modules was extend to arbitrary acts. Several statements that are equivalent to the cancellation (weak cancellation) property have been studied. Some characterizations of cancellation (weak cancellation) acts was presented and derive many of their properties. Using the condition of multiplication acts various results of cancellation (weak cancellation) acts are investigated.