Residual coordinates over one-dimensional rings

Given a noetherian ring Rand n >= 2, it is well-known that residual coordinates of the polynomial algebra R-[n] are m-stable coordinates for some m >= 1, that is they become coordinates in the larger polynomial algebra R[n+m]. In this paper we prove that, over a large class of noetherian one-dimensional rings, m = 1 is enough. This includes affine algebras over an algebraically closed field as well as noetherian complete local rings containing a field. (C) 2020 Elsevier B.V. All rights reserved.