This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS
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Second Edition S. Lang Algebraic Number Theory "This book is the second edition of Lang's famous and indispensable book on algebraic number theory. The major change from the previous edition is that the last chapter on explicit formulas has been completely rewritten. In addition, a few new sections have been added to the other chapters . . . Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—MATHEMATICAL REVIEWS
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This review is from: Algebraic Number Theory (Graduate Texts in Mathematics) (Hardcover)
Awesome text. For the more well-versed reader in Algebraic Number Theory. Great resource for a variety of topics.
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Inside This Book
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First Sentence:
This chapter describes the basic aspects of the ring of algebraic integers in a number field (always assumed to be of finite degree over the rational numbers Q). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
residue class field extension, admissible cycle, generalized ideal classes, modulo roots, ramification theorem, residue class degree, idele classes, multiplicative translation, class field theory, fractional ideal, archimedean absolute values, log mapping, finite separable extension, norm index, integral closure, ramified primes, decomposition group, restricted direct products, cyclotomic extensions, abelian extension, ideal class group, discrete valuation ring, multiplicative subset, ramification index, ramified extensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Theorem, Reine Angew New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter describes the basic aspects of the ring of algebraic integers in a number field (always assumed to be of finite degree over the rational numbers Q). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
residue class field extension, admissible cycle, generalized ideal classes, modulo roots, ramification theorem, residue class degree, idele classes, multiplicative translation, class field theory, fractional ideal, archimedean absolute values, log mapping, finite separable extension, norm index, integral closure, ramified primes, decomposition group, restricted direct products, cyclotomic extensions, abelian extension, ideal class group, discrete valuation ring, multiplicative subset, ramification index, ramified extensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Theorem, Reine Angew New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 34
books:
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100
books
cite this book:
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- Class Field Theory (Advanced Book Classics) by Emil Artin on 7 pages
- Basic Number Theory (Classics in Mathematics) by Andre Weil in Front Matter, page 177, and Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil on page 177, Back Matter (1), and Back Matter (2)
- Real and Functional Analysis (Graduate Texts in Mathematics) (v. 142) by Serge Lang in Front Matter, and Back Matter
- Algebraic Number Theory by H. Koch in Back Matter
See all 34 books this book cites
- Algebra by Serge Lang on 7 pages
- Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty on 5 pages
- Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards on 4 pages
- The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan on 4 pages
- One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) by Klaus-Jochen Engel in Back Matter (1), Back Matter (2), and Back Matter (3)
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