Research On The W^*-Modules Over Commutative Rings

In this thesis,we mainly study the related properties of^*-modules,and use the theory of^*-modules to characterize some classic rings.First,we introduce GV^*-torsion mod-ules,GV^*-torsion-free modules and^*-modules with the help of GV^*（）that is a set of regular GV-ideals（GV^*-ideals）,and give their basic properties and equivalent characterizations.Then,we introduce the conceptions of^*-closure of modules,prime^*-ideals and^*-finitely gen-erated modules.We indicate the correlativity between^*-modules and-modules,and prove the consistency of^*-ideals and-ideals over regular ideals.Finally,we give some new char-acterizations of-Noether rings and SM rings,and prove corresponding^*-theoretic analogue of the Cartan-Eilenberg-Bass theorem,that is,is a-Noether ring if and only if every direct sum of GV^*-torsion-free injective modules is injective;is an SM ring if and only if every direct sum of GV^*-torsion-free reg-injective modules is reg-injective.