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Abstract

In Section 5.2 of BA we saw that semisimple Artinian rings can be described quite explicitly as direct products of full matrix rings over skew fields (Wedderburn's theorem). Later in Chapters 7 and 8 we shall see what can be said when the Artinian hypothesis is dropped, but in many cases, such as the study of group algebras in finite characteristic, it is important to find out more about the non-semisimple (but Artinian) case. There is now a substantial theory of such algebras which is still developing, and a full treatment is beyond the framework of this book, but some of the basic properties are described here.

Keywords

Local Ring Direct Summand Left Ideal Projective Module Projective Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Professor P.M. Cohn 2003

Authors and Affiliations

  • P. M. Cohn
    • 1
  1. 1.Department of MathematicsUniversity College LondonLondon

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