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Let R be a PID. We construct and classify all coordinates of R[x,y] of theform p_2y+Q_2(p_1x+Q_1(y)) with p_1 and p_2 in qt(R) and Q_1 and Q_2 inqt(R)[y]. From this construction (with R=K[z]) we obtain non tame automorphismss of K[x,y,z] (where K is a field of characteristic 0) such that the sub-groupgenerated by s and the affine automorphisms contains all tame automorphisms.

Coordinates of R[x,y]: Constructions and classifications