ON THE OSOFSKY–SMITH THEOREM

摘要

We recall a version of the Osofsky–Smith theorem in the context of anGrothendieck category and derive several consequences of this result. For example, itnis deduced that every locally finitely generated Grothendieck category with a family ofncompletely injective finitely generated generators is semi-simple. We also discuss thentorsion-theoretic version of the classical Osofsky theorem which characterizes semi-nsimple rings as those rings whose every cyclic module is injective.