On certain classes of modules

Let X be a class or R-modules containing 0 and closed under isomorphic images. With any such X we associate three classes GX, FX and ?X. The study of some of the closure properties of these classes allows us to obtain characterization of Artinian modules dualizing results of Chatters. The theory of Dual Glodie dimension as developed by the author in some of his earlier work plays a crucial role in the present paper.