Hilbert's tenth problem :: diophantine classes and extensions to global fields /
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 int...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, UK ; New York :
Cambridge University Press,
2006.
|
| Series: | New mathematical monographs ;
7. |
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | 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. |
| Physical Description: | 1 online resource (xiii, 320 pages) |
| Bibliography: | Includes bibliographical references (pages 310-316) and index. |
| ISBN: | 9780511257407 0511257406 0521833604 9780521833608 0511255810 9780511255816 0511256906 9780511256905 0511256388 9780511256387 051154295X 9780511542954 |
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MARC
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Record in the Search Index
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| author | Shlapentokh, Alexandra |
| author_GND | http://id.loc.gov/authorities/names/nb2006024712 |
| author_facet | Shlapentokh, Alexandra |
| author_role | |
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| contents | Introduction -- Diophantine classes: definitions and basic facts -- Diophantine equivalence and Diophantine decidability -- Integrality at finitely many primes and divisibility of order at infinitely many primes -- Bound equations for number fields and their consequences -- Units of rings of W-integers of norm 1 -- Diophantine classes over number fields -- Diophantine undecidability of function fields -- Bounds for function fields -- Diophantine classes over function fields -- Mazur's conjectures and their consequences -- Results of Poonen -- Beyond global fields -- Recursion (computability) theory -- Number theory. |
| ctrlnum | (OCoLC)159933215 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn159933215 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:35:52Z |
| institution | BVB |
| isbn | 9780511257407 0511257406 0521833604 9780521833608 0511255810 9780511255816 0511256906 9780511256905 0511256388 9780511256387 051154295X 9780511542954 |
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| series | New mathematical monographs ; |
| series2 | New mathematical monographs ; |
| spelling | Shlapentokh, Alexandra. http://id.loc.gov/authorities/names/nb2006024712 Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh. Diophantine classes and extensions to global fields Cambridge, UK ; New York : Cambridge University Press, 2006. 1 online resource (xiii, 320 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier New mathematical monographs ; 7 Includes bibliographical references (pages 310-316) and index. Introduction -- Diophantine classes: definitions and basic facts -- Diophantine equivalence and Diophantine decidability -- Integrality at finitely many primes and divisibility of order at infinitely many primes -- Bound equations for number fields and their consequences -- Units of rings of W-integers of norm 1 -- Diophantine classes over number fields -- Diophantine undecidability of function fields -- Bounds for function fields -- Diophantine classes over function fields -- Mazur's conjectures and their consequences -- Results of Poonen -- Beyond global fields -- Recursion (computability) theory -- Number theory. Print version record. 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. Hilbert's tenth problem. http://id.loc.gov/authorities/subjects/sh93004733 Algebraic number theory. http://id.loc.gov/authorities/subjects/sh85003436 Diophantine equations. http://id.loc.gov/authorities/subjects/sh92001030 Dixième problème de Hilbert. Théorie algébrique des nombres. Équations diophantiennes. MATHEMATICS Number Theory. bisacsh Algebraic number theory fast Diophantine equations fast Hilbert's tenth problem fast has work: Hilbert's tenth problem (Text) https://id.oclc.org/worldcat/entity/E39PCGbVgMJRCDTddvP7hm9CHy https://id.oclc.org/worldcat/ontology/hasWork Print version: Shlapentokh, Alexandra. Hilbert's tenth problem. Cambridge, UK ; New York : Cambridge University Press, 2006 0521833604 9780521833608 (DLC) 2007360684 (OCoLC)75713026 New mathematical monographs ; 7. http://id.loc.gov/authorities/names/n2003010567 |
| spellingShingle | Shlapentokh, Alexandra Hilbert's tenth problem : diophantine classes and extensions to global fields / New mathematical monographs ; Introduction -- Diophantine classes: definitions and basic facts -- Diophantine equivalence and Diophantine decidability -- Integrality at finitely many primes and divisibility of order at infinitely many primes -- Bound equations for number fields and their consequences -- Units of rings of W-integers of norm 1 -- Diophantine classes over number fields -- Diophantine undecidability of function fields -- Bounds for function fields -- Diophantine classes over function fields -- Mazur's conjectures and their consequences -- Results of Poonen -- Beyond global fields -- Recursion (computability) theory -- Number theory. Hilbert's tenth problem. http://id.loc.gov/authorities/subjects/sh93004733 Algebraic number theory. http://id.loc.gov/authorities/subjects/sh85003436 Diophantine equations. http://id.loc.gov/authorities/subjects/sh92001030 Dixième problème de Hilbert. Théorie algébrique des nombres. Équations diophantiennes. MATHEMATICS Number Theory. bisacsh Algebraic number theory fast Diophantine equations fast Hilbert's tenth problem fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh93004733 http://id.loc.gov/authorities/subjects/sh85003436 http://id.loc.gov/authorities/subjects/sh92001030 |
| title | Hilbert's tenth problem : diophantine classes and extensions to global fields / |
| title_alt | Diophantine classes and extensions to global fields |
| title_auth | Hilbert's tenth problem : diophantine classes and extensions to global fields / |
| title_exact_search | Hilbert's tenth problem : diophantine classes and extensions to global fields / |
| title_full | Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh. |
| title_fullStr | Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh. |
| title_full_unstemmed | Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh. |
| title_short | Hilbert's tenth problem : |
| title_sort | hilbert s tenth problem diophantine classes and extensions to global fields |
| title_sub | diophantine classes and extensions to global fields / |
| topic | Hilbert's tenth problem. http://id.loc.gov/authorities/subjects/sh93004733 Algebraic number theory. http://id.loc.gov/authorities/subjects/sh85003436 Diophantine equations. http://id.loc.gov/authorities/subjects/sh92001030 Dixième problème de Hilbert. Théorie algébrique des nombres. Équations diophantiennes. MATHEMATICS Number Theory. bisacsh Algebraic number theory fast Diophantine equations fast Hilbert's tenth problem fast |
| topic_facet | Hilbert's tenth problem. Algebraic number theory. Diophantine equations. Dixième problème de Hilbert. Théorie algébrique des nombres. Équations diophantiennes. MATHEMATICS Number Theory. Algebraic number theory Diophantine equations Hilbert's tenth problem |
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