Hilbert's Tenth Problem (Hardcover)

Alexandra Shlapentokh

ISBN 10: 0521833604 / ISBN 13: 9780521833608

Verlag: Cambridge University Press, Cambridge, 2006

Hardcover. In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians 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. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers. Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Bestandsnummer des Verkäufers 9780521833608

Inhaltsangabe:

An account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.

Über die Autorin bzw. den Autor: Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.

Bibliografische Details

Titel: Hilbert's Tenth Problem (Hardcover)
Verlag: Cambridge University Press, Cambridge
Erscheinungsdatum: 2006
Einband: Hardcover
Zustand: new
Auflage: 1. Auflage