Interpolation in the Automorphism Group of a Polynomial Ring

Abstract

Let R be a commutative ring with unity and SAn(R) be the group of volume-preserving automorphisms of the polynomial R-algebra R[n]. Given a proper ideal 𝔞 of R, we address in this paper the question of whether the canonical group homomorphism SAn(R) → SAn(R/𝔞) is surjective. As an application, we retrieve and generalize, in a unified way, several known results on residual coordinates in polynomial rings.