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Number fields
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Marcus, Daniel A.
Number fields
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Number fieldsby Daniel A. Marcus.
作者:
Marcus, Daniel A.
出版者:
Cham :Springer International Publishing :2018.
面頁冊數:
xviii, 203 p. :digital ;24 cm.
Contained By:
Springer eBooks
標題:
Number theory.
電子資源:
http://dx.doi.org/10.1007/978-3-319-90233-3
ISBN:
9783319902333$q(electronic bk.)
Number fields
Marcus, Daniel A.
Number fields
[electronic resource] /by Daniel A. Marcus. - 2nd ed. - Cham :Springer International Publishing :2018. - xviii, 203 p. :digital ;24 cm. - Universitext,0172-5939. - Universitext..
1: A Special Case of Fermat's Conjecture -- 2: Number Fields and Number Rings -- 3: Prime Decomposition in Number Rings -- 4: Galois Theory Applied to Prime Decomposition -- 5: The Ideal Class Group and the Unit Group -- 6: The Distribution of Ideals in a Number Ring -- 7: The Dedekind Zeta Function and the Class Number Formula -- 8: The Distribution of Primes and an Introduction to Class Field Theory -- Appendix A: Commutative Rings and Ideals -- Appendix B: Galois Theory for Subfields of C -- Appendix C: Finite Fields and Rings -- Appendix D: Two Pages of Primes -- Further Reading -- Index of Theorems -- List of Symbols.
Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra. Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject. From the reviews: "A thoroughly delightful introduction to algebraic number theory" - Ezra Brown in the Mathematical Reviews "An excellent basis for an introductory graduate course in algebraic number theory" - Harold Edwards in the Bulletin of the American Mathematical Society.
ISBN: 9783319902333$q(electronic bk.)
Standard No.: 10.1007/978-3-319-90233-3doiSubjects--Topical Terms:
189521
Number theory.
LC Class. No.: QA241 / .M373 2018
Dewey Class. No.: 512.7
Number fields
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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.
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