𝑅-automorphisms of 𝑅[𝐺] for 𝐺 abelian torsion-free

Abstract

Let R R be a commutative ring with identity and G G a torsion-free abelian group. This note describes for a reduced R R the group of R R -automorphisms of the group ring R [ G ] R[G] when either R R has finitely many idempotents or G G has finite torsion-free rank. It also describes the R R -automorphisms of R [ G ] R[G] for a general R R and G G finitely generated free.