Curves and coherent Prüfer rings (Q607061)

The goal of the paper under review is to show, in constructive mathematics, that if \(k\) is a discrete field (that is, an explicit field with a zero test) and \(f\) an arbitrary polynomial in \(k[x,y]\) then the localization \((k[x,y]/(f))_{f_y}\) is always a coherent Prüfer ring, where \(f_y=\frac{\partial f}{\partial y}\). One important corollary is that \(k[x,y]/(f)\) is a coherent Prüfer ring whenever \(1=(f, f_x,f_y)\). The paper concludes with a {tt magma} program and some examples.