Research of quasi-Frobenius rings and representation theory

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This research in concerned with quasi-Frobenius rings and their representation theory. Allotting a portion of the project to each investigator, I studied the structures and representations of quasi-Frobenius rings and related rings. Consequently, we obtained the following results.1. We constructed an algorithm for deciding whether a given factor algebra of a polynomial ring over a field is quasi-Frobenius and implemented the algorithm to computers. By this method, we completely determined the isomorphism classes of commutative quasi-Frobenius algebras with radical cube zero.2. We determined the condition for extending modules to be closed under finite direct sums and investigated self-duality of Auslander rings of local serial rings.3. We studied the "Direct Finite" property of modules of von-Neumann regular rings with weak comparability axiom.4. We also obtained other related results to this research.