Algorithms for Calculating the Inverse of a Given R-Automorphism of R[x

Abstract

Let R be a commutative ring with identity, and let R[x] be the polynomial ring in one indeterminate x over R. We give algorithms for calculating σ−1(x), where σ is a given R-automorphism of R[x], thus answering a question raised in [2]. Needless to say, this problem is trivial for nonreduced rings R, since an R-automorphism σ of R[x] in this case must have the simple form σ(x) = ux + c, where u, c ∈ R and where u is a unit.