2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113869We study z-automorphisms of the polynomial algebra K[x,y,z] and the free associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For K<x,y,z> we include also results about the structure of the z-tame automorphisms and algorithms which recognize z-tame automorphisms and z-tame coordinates.Rings and AlgebrasCommutative AlgebraPrimary 16S10. Secondary 16W20; 16Z05; 13B10; 13B25; 14E07text