Course in algebraic number theory

By:

Ash, Robert B

Publication details: Dover Publications, 2003. New York:Description: viii, 112 p. ; pb; 23 cmISBN:

9780486477541

Subject(s):

DDC classification:

512.74 ASH

Summary: This graduate-level text provides coverage for a one-semester course in algebraic number theory. It explores the general theory of factorization of ideals in Dedekind domains as well as the number field case. Detailed calculations illustrate the use of Kummer's theorem on lifting of prime ideals in extension fields. The author provides sufficient details for students to navigate the intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics include the factorization of prime ideals in Galois extensions and local as well as global fields, including the Artin-Whaples approximation theorem and Hensel's lemma. The text concludes with three helpful appendixes. Geared toward mathematics majors, this course requires a background in graduate-level algebra and a familiarity with integral extensions and localization.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	512.74 ASH (Browse shelf(Opens below))	1	Available		029855

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Previous	512.73 HAR Prime-detecting Sieves	512.73 MUR Problems in analytic number theory	512.73 QUE Diophantine approximation and dirichlet series	512.74 ASH Course in algebraic number theory	512.74 GOL Automorphic forms and L-functions for the group GL(n,R)	512.74 HAD Field theory and its classical problems, vol.19	512.74 KED p-adic differential equations	Next

Includes bibliographical references and index.

This graduate-level text provides coverage for a one-semester course in algebraic number theory. It explores the general theory of factorization of ideals in Dedekind domains as well as the number field case. Detailed calculations illustrate the use of Kummer's theorem on lifting of prime ideals in extension fields. The author provides sufficient details for students to navigate the intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics include the factorization of prime ideals in Galois extensions and local as well as global fields, including the Artin-Whaples approximation theorem and Hensel's lemma. The text concludes with three helpful appendixes. Geared toward mathematics majors, this course requires a background in graduate-level algebra and a familiarity with integral extensions and localization.

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