Lectures on Topics in Algebraic Number Theory
by Sudhir R. Ghorpade
Publisher: Indian Institute of Technology, Bombay 2002
Number of pages: 83
These lectures are aimed at giving 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.
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by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
by Robert B. Ash - University of Illinois
Basic course in algebraic number theory. It covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.
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 William Stein - University of Washington
Topics in this book: Rings of integers of number fields; Unique factorization of ideals in Dedekind domains; Structure of the group of units of the ring of integers; Finiteness of the group of equivalence classes of ideals of the ring of integers...