Abstract:

Let R be a retract of k［x,y,z］ with a retraction φ. It is proved that there exist p,q∈R such that R=k［p,q］ if
 the transcendental degree of R over k is 2 and either of the following  conditions holds: 1) R is an inert subalgebra containing no coordinates andφ is the gradient of a polynomial; 2) R is a 2valuation algebra.

Key words: retract, 2-valuation algebra, inert subalgebra