2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128264We study the class of 2-dimensional affine k-domains R satisfying ML(R) = k, where k is an arbitrary field of characteristic zero. In particular, we obtain the following result: Let R be a localization of a polynomial ring in finitely many variables over a field of characteristic zero. If ML(R) = K for some field K included in R and such that R has transcendence degree 2 over K, then R is K-isomorphic to K[X,Y,Z]/(XY-P(Z)) for some nonconstant polynomial P(Z) in K[Z].12 pages. See also http://aix1.uottawa.ca/~ddaigle/index.htmlAlgebraic GeometryCommutative Algebra14R10; 14R05; 14R20text