Invariant maximal ideals in group algebras
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- by Daniel R. Farkas PDF
- Proc. Amer. Math. Soc. 97 (1986), 569-576 Request permission
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
- Daniel R. Farkas, Toward multiplicative invariant theory, Group actions on rings (Brunswick, Maine, 1984) Contemp. Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 69–80. MR 810644, DOI 10.1090/conm/043/810644
- J. E. Roseblade, Group rings of polycyclic groups, J. Pure Appl. Algebra 3 (1973), 307–328. MR 332944, DOI 10.1016/0022-4049(73)90034-0
Additional Information
- © Copyright 1986 American Mathematical Society
- 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