EXTENSIONS OF DRINFELD MODULES OF RANK 2 BY THE CARLITZ MODULE

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.