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Invariant ideals of abelian group algebras under the multiplicative action of a field. I

Authors: D. S. Passman and A. E. Zalesskii
Journal: Proc. Amer. Math. Soc. 130 (2002), 939-949
MSC (2000): Primary 16S34, 12E20
Published electronically: November 9, 2001
MathSciNet review: 1873765
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Abstract: Let $D$ be a division ring and let $V=D^n$ be a finite-dimensional $D$-vector space, viewed multiplicatively. If $G=D^\bullet$is the multiplicative group of $D$, then $G$ acts on $V$ and hence on any group algebra $K[V]$. Our goal is to completely describe the semiprime $G$-stable ideals of $K[V]$. As it turns out, this result follows fairly easily from the corresponding results for the field of rational numbers (due to Brookes and Evans) and for infinite locally-finite fields. Part I of this work is concerned with the latter situation, while Part II deals with arbitrary division rings.

References [Enhancements On Off] (What's this?)

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Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

A. E. Zalesskii
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom

Received by editor(s): October 3, 2000
Published electronically: November 9, 2001
Additional Notes: The first author’s research was supported in part by NSF Grant DMS-9820271. Much of this work was performed during the second author’s visit to the University of Wisconsin-Madison, made possible by the financial support of EPSRC
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 American Mathematical Society