This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Edo, Ericvan den Essen, ArnoMaubach, Stefan2019-06-2820081864-7596https://doi.org/10.34657/1876https://oa.tib.eu/renate/handle/123456789/2651We prove that for a polynomial f 2 k[x, y, z] equivalent are: (1)f is a k[z]-coordinate of k[z][x, y], and (2) k[x, y, z]/(f) = k[2] and f(x, y, a) is a coordinate in k[x, y] for some a 2 k. This solves a special case of the Abhyankar-Sathaye conjecture. As a consequence we see that a coordinate f 2 k[x, y, z] which is also a k(z)-coordinate, is a [z]-coordinate. We discuss a method for onstructing automorphisms of k[x, y, z], and observe that the Nagata automorphism occurs naturally as the first non-trivial automorphism obtained by this method essentially linking Nagata with a non-tame R-automorphism of R[x], where R = k[z]/(z2).application/pdfeng510Report