Number fields

by Marcus, Daniel A.

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Title Statements

Full title :Number fields / Daniel A. Marcus.

Summary

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra. Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject. From the reviews: "A thoroughly delightful introduction to algebraic number theory"--Ezra Brown in the Mathematical Reviews "An excellent basis for an introductory graduate course in algebraic number theory"--Harold Edwards in the Bulletin of the American Mathematical Society

Edition Statements

Publication Date:2018.
Edition:Second edition

Publication Statements

Publisher(s):Springer
Place of Publication:Cham, Switzerland
Language:eng
Publication Date:2018.

The Physical Object

Description:1 online resource (xviii, 203 pages)

Edition Identifiers

ISBN:9783319902333, 3319902334
DOI:10.1007/978-3-319-90233-3
oclc:on1044745839
LC Classification:QA241
Dewey Decimal:512.7

1: A Special Case of Fermat's Conjecture -- 2: Number Fields and Number Rings -- 3: Prime Decomposition in Number Rings -- 4: Galois Theory Applied to Prime Decomposition -- 5: The Ideal Class Group and the Unit Group -- 6: The Distribution of Ideals in a Number Ring -- 7: The Dedekind Zeta Function and the Class Number Formula -- 8: The Distribution of Primes and an Introduction to Class Field Theory -- Appendix A: Commutative Rings and Ideals -- Appendix B: Galois Theory for Subfields of C -- Appendix C: Finite Fields and Rings -- Appendix D: Two Pages of Primes -- Further Reading -- Index of Theorems -- List of Symbols.