Oliynyk R. Radicals and torsion theory in the category to sets for semigroup act

This thesis is devoted to the radicals and the torsions in the category of acts over a monoid with zero. Necessary and sufficient conditions are determined for the class of monoids, when the lattice of quasi-filters and sigma quasi-filters will be two-element. The task of preradicals' triviality was solved in the category of acts. It was proved that in the category of acts all the preradicals are trivial if and only if monoid is a group with zero. It is also shown that the similar result holds in these categories: a) the category of all left acts, b) the Wiegandt-Lex category of acts, and c) the category of the multiplication acts.