On preradicals and closure operators in S -act

The present paper rests on the correspondence between idempotent closure operators and the generalized notion of radicals in the category of S -acts, S-Act. This correspondence in the semi-abelian categories is established as well as in the category of R-modules. In fact, the presence of a zero object in a semi-abelin category provides the tools necessary for pursuing the same correspondence between closure operators and radicals. But, here we construct the same correspondence in the nonsemi- abelian category S-Act.