This book presents an account of results extending <strong>Hilbert's Tenth Problem</strong> to integrally closed subrings of global fields.In the late sixties D... » 

This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.In the late sixties Davis, Matiyasevich, Putnam and Robinson showed that there was no algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. «