Preradical and kernel functors over categories of $S$-acts

We concider the big lattices of preradicals and kernel functors over some cathegories of centered $S$-acts, where $S$ is monoid whit zero. We prove that those big lattices are two elements if and only if monoid $S$ is groups with zero. A subset of a Rees generated pretorsion theory is a subquantale of quantale of pretorsion theory.