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This book provides an elementary, complete account of quasi-Frobenius 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 present extent of the theory is wide-ranging.
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QUASI-FROBENIUS RINGS
The study of quasi-Frobenius rings grew out of the theory of group representations in the 1940s and has produced an enormous body of results. This book makes no attempt to be encyclopedic but provides an elementary account of the basic facts about these rings at a level allowing researchers and graduate students to gain entry to the field. Many earlier results about self-injective rings are extended to the much wider class of mininjective rings; the methods used unify and simplify what is known in the area and so bring the reader up to current research. Sufficient background knowledge can be found in standard texts on noncommutative rings. However, appendices on Morita equivalence; on perfect, semiperfect, and semiregular rings; and on the Camps–Dicks theorem are included to make the book self-contained. After the basic results are established in Chapters 1 through 6, recent work is reviewed on three open problems in the field (the Faith conjecture, the FGF-conjecture, and the Faith– Menal conjecture). Some new results are provided and new and old methods for attacking these problems are outlined in an easily accessible format. W. K. Nicholson is Professor of Mathematics at the University of Calgary. M. F. Yousif is Professor of Mathematics at The Ohio State University.
CAMBRIDGE TRACTS IN MATHEMATICS General