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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Invariant maximal ideals in group algebras

Author: Daniel R. Farkas
Journal: Proc. Amer. Math. Soc. 97 (1986), 569-576
MSC: Primary 16A27
MathSciNet review: 845967
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Abstract: Given a finitely generated torsion free abelian group $ A$, any group of automorphisms of $ A$ extends to a group of algebra automorphisms of the group ring $ {{\mathbf{F}}_p}[A]$. When the automorphism group is cyclic, Roseblade has proved that $ {{\mathbf{F}}_p}[A]$ has infinitely many invariant maximal ideals. We count these ideals with a localized generating function which turns out to be rational.

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

  • [1] D. R. Farkas, Toward multiplicative invariant theory, Group Actions on Rings, Contemp. Math., vol. 43, Amer. Math. Soc., Providence, R. I., 1985. MR 810644 (87b:16013)
  • [2] J. E. Roseblade, Group rings of polycyclic groups, J. Pure Appl. Algebra 3 (1973), 307-328. MR 0332944 (48:11269)

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Keywords: Group algebra, characters, matrices over a finite ring
Article copyright: © Copyright 1986 American Mathematical Society

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