In this paper we prove the inheritance of polynomial identities by covers of nondegenerate Jordan algebras satisfying certain ideal absorption properties. As a consequence we obtain the inheritance of speciality by Martindale-like covers, proving, in part

We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or kω-spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences.