Radical and essential congruences on the category of S -act

In this paper, we study on torsion theory and radicals in the category of S -Act. We introduce the Kurosh-Amitsur radicals and the Hoehnke radicals. We then investigate the relationship between Hoehnke radicals and Kurosh-Amitsur radicals and we show that the class of Kurosh-Amitsur radicals as a poset is a reflective subcategory of the class of Hoehnke radicals. We also characterize the hereditary Kurosh-Amitsur radicals by the semisimple classes which are closed under taking injective envelop.