  We introduce and study "quasidualizing" modules. An artinian R-module T is
quasidualizing if the homothety map \hat R\rightarrow Hom(T,T) is an
isomorphism and Ext_R^i(T,T)=0 for each integer i>0. Quasidualizing modules are
associated to semidualizing modules via Matlis duality. We investigate the
associations via Matlis duality between subclasses of the Auslander class and
Bass class and subclasses of derived T-reflexive modules.
