The Radical

  • Richard S. Pierce
Part of the Graduate Texts in Mathematics book series (GTM, volume 88)


Wedderburn’s Theorem shows that the class of semisimple algebras is very limited. On the other hand, Proposition 3.1a suggests that Artinian algebras are semisimple “up to a radical.” In fact, this is the case. All that is missing from a proof is the result that rad A A is an ideal. We will establish this fact in Section 4.1. The rest of the chapter is concerned with properties and characterizations of the radical, a theorem about nilpotent algebras, and the radicals of group algebras.


Prime Ideal Left Ideal Group Algebra Division Algebra Nilpotent Element 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Richard S. Pierce
    • 1
  1. 1.University of ArizonaTucsonUSA

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