The Act Of An Operator

In this paper we will study some of the properties of an operator by looking at the associated S-act of this operator, and conversely. We look at some operators, like one to one operators, onto operators. On the other hand, we look at some act theoretic concepts, like faithful acts, finitely generated acts, singular acts, separated acts, torsion free acts and noetherian acts. We try to determine what properties of T make the associated S-act has any of these properties.