Exactness of the double dual

Abstract

Let R R be an artinian ring. The double R R -dual ( )** preserves monomorphisms, is left exact, or is right exact if and only if R R is QF- 3 3 , has dominant dimension at least 2, or is QF, respectively. Furthermore, both double dual functors preserve epimorphisms of finitely generated (left and right) modules if and only if both dual functors ( )* are exact on short exact sequences of finitely generated torsionless modules, and these conditions are equivalent to finitely generated torsionless modules being reflexive.