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The theory of classical valuations

The theory of classical valuations

Material type
Personal Author
Ribenboim, Paulo.
Title Statement
The theory of classical valuations / Paulo Ribenboim.
Publication, Distribution, etc
New York :   Springer,   c1999.  
Physical Medium
ix, 403 p. ; 25 cm.
0387985255 (hardcover : alk. paper)
Bibliography, Etc. Note
Includes bibliographical references (p. 391-393) and index.
Subject Added Entry-Topical Term
Algebraic fields. Valuation theory.
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008 980330s1999 nyu b 001 0 eng
010 ▼a 98004349
020 ▼a 0387985255 (hardcover : alk. paper)
040 ▼a DLC ▼c DLC ▼d C#P ▼d OHX ▼d NLC ▼d 211009
049 1 ▼l 111181377
050 0 0 ▼a QA247 ▼b .R483 1999
055 0 1 ▼a QA247
082 0 0 ▼a 512/.3 ▼2 21
090 ▼a 512.3 ▼b R484t
100 1 ▼a Ribenboim, Paulo.
245 1 4 ▼a The theory of classical valuations / ▼c Paulo Ribenboim.
260 ▼a New York : ▼b Springer, ▼c c1999.
300 ▼a ix, 403 p. ; ▼c 25 cm.
504 ▼a Includes bibliographical references (p. 391-393) and index.
650 0 ▼a Algebraic fields.
650 0 ▼a Valuation theory.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.3 R484t Accession No. 111181377 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

1 Absolute Values of Fields.- 1.1. First Examples.- 1.2. Generalities About Absolute Values of a Field.- 1.3. Absolute Values of Q.- 1.4. The Independence of Absolute Values.- 1.5. The Topology of Valued Fields.- 1.6. Archimedean Absolute Values.- 1.7. Topological Characterizations of Valued Fields.- 2 Valuations of a Field.- 2.1. Generalities About Valuations of a Field.- 2.2. Complete Valued Fields and Qp.- 3 Polynomials and Henselian Valued Fields.- 3.1. Polynomials over Valued Fields.- 3.2. Henselian Valued Fields.- 4 Extensions of Valuations.- 4.1. Existence of Extensions and General Results.- 4.2. The Set of Extensions of a Valuation.- 5 Uniqueness of Extensions of Valuations and Poly-Complete Fields.- 5.1. Uniqueness of Extensions.- 5.2. Poly-Complete Fields.- 6 Extensions of Valuations: Numerical Relations.- 6.1. Numerical Relations for Valuations with Unique Extension.- 6.2. Numerical Relations in the General Case.- 6.3. Some Interesting Examples.- 6.4. Appendix on p-Groups.- 7 Power Series and the Structure of Complete Valued Fields.- 7.1. Power Series.- 7.2. Structure of Complete Discrete Valued Fields.- 8 Decomposition and Inertia Theory.- 8.1. Decomposition Theory.- 8.2. Inertia Theory.- 9 Ramification Theory.- 9.1. Lower Ramification Theory.- 9.2. Higher Ramification.- 10 Valuation Characterizations of Dedekind Domains.- 10.1. Valuation Properties of the Rings of Algebraic Integers.- 10.2. Characterizations of Dedekind Domains.- 10.3. Characterizations of Valuation Domains.- 11 Galois Groups of Algebraic Extensions of Infinite Degree.- 11.1. Galois Extensions of Infinite Degree.- 11.2. The Abelian Closure of Q.- 12 Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over Q.- 12.1. Ideals.- 12.2. Valuations, Dedekind Domains, and Examples.- 12.3. Divisors of Algebraic Number Fields of Infinite Degree.- 13 A Glimpse of Krull Valuations.- 13.1. Generalities.- 13.2. Integrally Closed Domains.- 13.3. Suggestions for Further Study.- Appendix Commutative Fields and Characters of Finite Abelian Groups.- A.1. Algebraic Elements.- A.2. Algebraic Elements, Algebraically Closed Fields.- A.3. Algebraic Number Fields.- A.4. Characteristic and Prime Fields.- A.5. Normal Extensions and Splitting Fields.- A.6. Separable Extensions.- A.7. Galois Extensions.- A.8. Roots of Unity.- A.9. Finite Fields.- A.10. Trace and Norm of Elements.- A.11. The Discriminant.- A.12. Discriminant and Resultant of Polynomials.- A.13. Inseparable Extensions.- A.14. Perfect Fields.- A.15. The Theorem of Steinitz.- A.16. Orderable Fields.- A.17. The Theorem of Artin.- A.18. Characters of Finite Abelian Groups.

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