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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
DOI: https://doi.org/10.1090/S0002-9939-1986-0845967-5
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.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0845967-5
Keywords: Group algebra, characters, matrices over a finite ring
Article copyright: © Copyright 1986 American Mathematical Society