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- catalog abstract ""In the second half of the last century, Kummer introduced "local" methods in his study of Fermat's last theorem. Hensel constructed the p-adic numbers and proved the so-called "Hensel lemma." Kurschak formally introduced the concept of a valuation of a field, and Ostrowski, Hasse, Schmidt, Krull, and others developed the theory. These classical valuations play a central cental role in the study of number fields and algebraic functions of one variable." "The present book is one of the first texts in English devoted to the beautiful theory of classical valuations. The book is self-contained and up-to-date, and proofs are given in full detail. Thus, it will be an invaluable resource for graduate students and research mathematicians."--BOOK JACKET.".
- catalog contributor b11329875.
- catalog created "c1999.".
- catalog date "1999".
- catalog date "c1999.".
- catalog dateCopyrighted "c1999.".
- catalog description ""In the second half of the last century, Kummer introduced "local" methods in his study of Fermat's last theorem. Hensel constructed the p-adic numbers and proved the so-called "Hensel lemma." Kurschak formally introduced the concept of a valuation of a field, and Ostrowski, Hasse, Schmidt, Krull, and others developed the theory. These classical valuations play a central cental role in the study of number fields and algebraic functions of one variable." "The present book is one of the first texts in English devoted to the beautiful theory of classical valuations. The book is self-contained and up-to-date, and proofs are given in full detail. Thus, it will be an invaluable resource for graduate students and research mathematicians."--BOOK JACKET.".
- catalog description "Ch. 1. Absolute Values of Fields -- Ch. 2. Valuations of a Field -- Ch. 3. Polynomials and Henselian Valued Fields -- Ch. 4. Extensions of Valuations -- Ch. 5. Uniqueness of Extensions of Valuations and Poly-Complete Fields -- Ch. 6. Extensions of Valuations: Numerical Relations -- Ch. 7. Power Series and the Structure of Complete Valued Fields -- Ch. 8. Decomposition and Inertia Theory -- Ch. 9. Ramification Theory -- Ch. 10. Valuation Characterizations of Dedekind Domains -- Ch. 11. Galois Groups of Algebraic Extensions of Infinite Degree -- Ch. 12. Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over Q -- Ch. 13. A Glimpse of Krull Valuations -- App. Commutative Fields and Characters of Finite Abelian Groups.".
- catalog description "Includes bibliographical references (p. 391-393) and index.".
- catalog extent "ix, 403 p. ;".
- catalog identifier "0387985255 (hardcover : alk. paper)".
- catalog issued "1999".
- catalog issued "c1999.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "512/.3 21".
- catalog subject "Algebraic fields.".
- catalog subject "QA247 .R483 1999".
- catalog subject "Valuation theory.".
- catalog tableOfContents "Ch. 1. Absolute Values of Fields -- Ch. 2. Valuations of a Field -- Ch. 3. Polynomials and Henselian Valued Fields -- Ch. 4. Extensions of Valuations -- Ch. 5. Uniqueness of Extensions of Valuations and Poly-Complete Fields -- Ch. 6. Extensions of Valuations: Numerical Relations -- Ch. 7. Power Series and the Structure of Complete Valued Fields -- Ch. 8. Decomposition and Inertia Theory -- Ch. 9. Ramification Theory -- Ch. 10. Valuation Characterizations of Dedekind Domains -- Ch. 11. Galois Groups of Algebraic Extensions of Infinite Degree -- Ch. 12. Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over Q -- Ch. 13. A Glimpse of Krull Valuations -- App. Commutative Fields and Characters of Finite Abelian Groups.".
- catalog title "The theory of classical valuations / Paulo Ribenboim.".
- catalog type "text".