Quasi-Frobenius Rings
Seiten
2003
Cambridge University Press (Verlag)
978-0-521-81593-2 (ISBN)
Cambridge University Press (Verlag)
978-0-521-81593-2 (ISBN)
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.
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.
| Erscheint lt. Verlag | 8.9.2003 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Mathematics |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 160 x 236 mm |
| Gewicht | 600 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-521-81593-2 / 0521815932 |
| ISBN-13 | 978-0-521-81593-2 / 9780521815932 |
| Zustand | Neuware |
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