The Jacobson Radical

  • Benson Farb
  • R. Keith Dennis
Part of the Graduate Texts in Mathematics book series (GTM, volume 144)


In Chapter One we developed a structure theory for semisimple rings, as summarized in Theorem 1.18. This theory used, for the most part, properties of modules over a semisimple ring in order to characterize such a ring. In this chapter, we give a more intrinsic characterization of semisimple rings.


Local Ring Left Ideal Division Ring Nilpotent Element Matrix Ring 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Benson Farb
    • 1
  • R. Keith Dennis
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

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