Explicit generators of the invariants of finite groups

Abstract

Let R denote a commutative (and associative) ring with 1 and let A denote a finitely generated commutative R-algebra. Let G denote a finite group of R-algebra automorphisms of A. In the case that R is a field of characteristic 0, Noether constructed a finite set of R-algebra generators of the invariants of G. This paper proves that the same construction produces a set of generators of the invariants of G when \G\! is invertible in R. Generators of the invariants of G are also explicitly described in the case that G is solvable and \G\ is invertible in R. © 1996 Academic Press, Inc.