A Hoehnke Radical on the Topos Act-s

One of the important concepts in topos theory is the concept of (weak) Lawvere-Tierney topology. A class of (weak) Lawvere topology on the  topos  Act-S of right acts over a  fixed monoid S is ideal topology which has been introduced by the authors in [13]. In this paper we first give some characterizations of sheaves with respect to this kind of topologies. Then, using this topology, we construct a Hoehnke radical on this topos. Finally, we investigate the relationship between the corresponding sheaf to the closure operator obtained from this radical and the corresponding sheaf with respect to the ideal topology../files/site1/files/61/13Abstract.pdf