On duality theory and AB5* modules Original Research Article

Let R-Mod be the category of unital left modules over a ring R. It is shown that a finitely closed subcategory image of R-Mod is an AB5* category if and only if image is dual to some finitely closed subcategory of Mod-T, for a suitable ring T. From this it follows that, for any R-module M, the Grothendieck category σ[M] has a Morita duality in the sense of Anh and Wiegandt if and only if M is a locally AB5*, i.e., every finitely generated module in σ[M] satisfies AB5*. Moreover, it is proved that a module M is linearly compact in σ[M] if and only if every finite direct sum Mn is an AB5* module.