A Course In Algebraic Number Theory
by Robert B. Ash
Publisher: University of Illinois 2003
This is a text for a basic course in algebraic number theory, written to provide reasonable coverage for a one-semester course. The text covers the general theory of factorization of ideals in Dedekind domains, detailed calculations illustrating the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc. A standard graduate course in algebra is assumed as prerequisite.
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by Steve Wright - arXiv
This is a series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required.
by J.S. Milne
Contents: Preliminaries From Commutative Algebra; Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Valuations; Local Fields; Global Fields.
by J. S. Milne
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These lecture notes give a rapid introduction to some basic aspects of Algebraic Number Theory with as few prerequisites as possible. Topics: Field Extensions; Ring Extensions; Dedekind Domains and Ramification Theory; Class Number and Lattices.