On radical and torsion theory in the category of S-acts

In abelian categories like the category of R-modules and even in the category S-Act 0 of S-acts with a unique zero, idempotent radicals and torsion theories are equivalent, and the { \tau}-torsion and { \tau}- torsion free classes of a torsion theory { \tau} are closed under coproducts. These are not necessarily true in the category S-Act of S-acts. In this paper, we prove that torsion theories are equivalent with the Kurosh- Amitsur radicals. We, also, show that the class of Kurosh-Amitsur radicals is a reflective subcategory of Hoehnke radicals, as a poset.

Categories: math.RT math.RA