Description

Provides an elementary account of the basic facts about quasi-Frobenius rings. A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian. While the present extent of the theory of these rings is vast, this book provides a self-contained account at a level allowing researchers and graduate students to gain entry to the field. A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian. While the present extent of the theory of these rings is vast, this book provides a self-contained account at a level allowing researchers and graduate students to gain entry to the field. A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all four combinations are equivalent). The study of these rings grew out of the theory of representations of a finite group as a group of matrices over a field, and the subject is intimately related to duality, the duality from right to left modules induced by the hom functor and the duality related to annihilators. The present extent of the theory is vast, and this book makes no attempt to be encyclopedic; instead it provides an elementary, self-contained account of the basic facts about these rings at a level allowing researchers and graduate students to gain entry to the field. 1. Background; 2. Mininjective rings; 3. Semiperfect mininjective rings; 4. Min-CS rings; 5. Principally injective and FP-rings; 6. Simple-injective and dual rings; 7. FGF rings; 8. Johns rings; 9. A generic example; Appendix A. Morita equivalence; Appendix B. Semiperfect and semiregular rings; Appendix C. The Camps-Dicks theorem. 'Summing up, this book is a research monograph with up-to-date information on QF-rings and provides a self-contained and very readable introduction to the topics …'. Zentralblatt MATH 'The authors have achieved two seemingly incompatible goals: to provide an elementary introduction to the classical theory of quasi-Frobenius rings, and to bring the reader up to the current research in the field. This makes the book interesting both for graduate students and researchers in contemporary module theory.' EMS Newsletter