Back to School Savings: Save up to 30% on print books and eBooks. No promo code needed.
Back to School Savings: Save up to 30%
The Jacobson Radical of Group Algebras
1st Edition - April 1, 1987
Author: G. Karpilovsky
9 7 8 - 0 - 0 8 - 0 8 7 2 4 6 - 9
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… Read more
Save 50% on book bundles
Immediately download your ebook while waiting for your print delivery. No promo code is needed.
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.
Ring-Theoretic Background. Group Algebras and Their Modules. The Jacobson Radical of Group Algebras: Foundations of the Theory. Group Algebras of p-Groups over Fields of Characteristic p. The Jacobson Radical and Induced Modules. The Loewy Length of Projective Modules. The Nilpotency Index. Radicals of Blocks. Bibliography. Index.
No. of pages: 531
Published: April 1, 1987
Imprint: North Holland
eBook ISBN: 9780080872469
Affiliations and expertise
California State University, Department of Mathematics, Chico, CA, USA