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

Passman, D.; Zalesskiĭ, A.

doi:10.1090/S0002-9939-01-06092-0

Invariant ideals of abelian group algebras under the multiplicative action of a field. I
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by D. S. Passman and A. E. Zalesskiĭ PDF

Proc. Amer. Math. Soc. 130 (2002), 939-949 Request permission

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

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