A characterization of cylinderlike surfaces (Q1320970)

A cylinderlike surface is an affine, rational, nonsingular surface, \(T = \text{Spec} A\), over an algebraic closed field \(k\) of characteristic zero having the properties that \(A^* = k^*\), \(\text{Pic} T\) is torsion and \(T\) contains a nonempty subset \(U\) which is isomorphic to \(\mathbb{A}^ 1 \times C\) where \(C\) is a rational curve. In the paper under review the author gives a characterization of cylinderlike surfaces. In fact an explicit description of the rings whose spectra are cylinderlike surfaces is given.