Semisimple Modules & Rings and the Wedderburn Structure Theorem

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


This chapter is concerned with looking at part of a structure theory for rings. The idea of any “structure theory” of an object (in this case a ring) is to express that object in terms of simpler, better understood pieces. For example, the Wedderburn Structure Theorem says that any semisimple ring (we’ll define this later) is isomorphic to a finite product of matrix rings over division rings, each of which is simple. The theory for semisimple modules is in many ways analogous to the theory of vector spaces over a field, where we can break up vector spaces as sums of certain subspaces.


Direct Summand Left Ideal Simple Module Division Ring 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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