Direct sums of reflexive modules Original Research Article

The problem of determining when reflexivity is inherited by direct sums of reflexive modules over finite dimensional split algebras is addressed. We show that this holds if the algebra is left locally distributive, a class of algebras which includes serial algebras, as well as for those algebras R with radical J and a basic set of idempotents such that dim(eJf) ≤ 3 for all idempotents e, f in the set. In the opposite direction, it is proved that a necessary condition for direct sums of reflexive modules to be reflexive is that the quiver of the algebra should contain no triple arrows.