Frobenius and Quasi-Frobenius Rings

  • T. Y. Lam
Part of the Graduate Texts in Mathematics book series (GTM, volume 189)


The class of rings that are self-injective (as a left or right module over themselves) has been under close scrutiny by ring theorists. There is a vast literature on the structure of self-injective rings satisfying various other conditions. In a book of limited ambition such as this, it would be difficult to do justice to this extensive literature. As a compromise, we focus our attention in this chapter on a special class of such rings called quasi-Frobenius (QF) rings, and the subclass of Frobenius rings. It will be seen that the finite-dimensional Frobenius algebras discussed in §3B are examples of the latter.


Left Ideal Division Ring Cartan Matrix Artinian Ring Symmetric Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • T. Y. Lam
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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