Preradical and kernel functors over categories of S−acts

Abstract

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.