000			01433 a2200193 4500
999			_c53492 _d53492
008			210101b ||||| |||| 00| 0 eng d
020			_a9780486477541
082			_a512.74 _bASH
100			_aAsh, Robert B.
245			_aCourse in algebraic number theory
260			_bDover Publications, _c2003. _aNew York:
300			_a viii, 112 p. ; _bpb; _c23 cm.
365			_aUSD _b10.95
504			_aIncludes bibliographical references and index.
520			_aThis 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.
650			_aMathematics- Algebra
650			_aAlgebraic Number Theory
942			_2ddc _cTD