$R$-automorphisms of $R[G]$ for $G$ abelian torsion-free
HTML articles powered by AMS MathViewer
- by David C. Lantz PDF
- Proc. Amer. Math. Soc. 61 (1976), 1-6 Request permission
Abstract:
Let $R$ be a commutative ring with identity and $G$ a torsion-free abelian group. This note describes for a reduced $R$ the group of $R$-automorphisms of the group ring $R[G]$ when either $R$ has finitely many idempotents or $G$ has finite torsion-free rank. It also describes the $R$-automorphisms of $R[G]$ for a general $R$ and $G$ finitely generated free.References
- J. W. Brewer and E. A. Rutter, Isomorphic polynomial rings, Arch. Math. (Basel) 23 (1972), 484–488. MR 320068, DOI 10.1007/BF01304919
- Robert W. Gilmer Jr., $R$-automorphisms of $R[X]$, Proc. London Math. Soc. (3) 18 (1968), 328–336. MR 229633, DOI 10.1112/plms/s3-18.2.328
- Graham. Higman, The units of group-rings, Proc. London Math. Soc. (2) 46 (1940), 231–248. MR 2137, DOI 10.1112/plms/s2-46.1.231
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 1-6
- MSC: Primary 13F20; Secondary 13B10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0435060-1
- MathSciNet review: 0435060