### The Jacobson radical of group algebras [E-Book] / Gregory Karpilovsky.

##### **The Jacobson radical of group algebras [E-Book] / Gregory Karpilovsky. **

Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two dec...

Personal Name(s): | Karpilovsky, Gregory, |
---|---|

Imprint: |
Amsterdam ; New York : New York, N.Y., U.S.A. :
North-Holland ;
1987
Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., |

Physical Description: |
1 online resource (x, 532 p.) |

Note: |
englisch |

ISBN: |
9780444701909 0444701907 |

Series Title: |
North-Holland mathematics studies ;
135 Notas de matematica ; 115 |

Subject (LOC): | |

Full Text |

Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results. The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest. |