Algebraic Number Theory - James Milne

Algebraic Number Theory Milne Version March 18, 2017. An Algebraic Number field is a finite extension of Q; an Algebraic Number is an element of an Algebraic Number field. Algebraic Number Theory studies the arithmetic of Algebraic Number fields the ring of integers in the Number field, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on. An abelian extension of a field is a Galois extension of the field with abelian Galois group. Class field Theory describes the abelian extensions of a Number field in terms of the arithmetic of the field. These notes are concerned with Algebraic Number Theory , and the sequel with class field Theory . BibTeX information @misc{milneANT, author={ Milne , James S.}}

He wrote a very influential book on algebraic number theory in 1897, which gave the first systematic account of the theory. Some of his famous problems were on number theory, and have also been influential. TAKAGI (1875–1960). He proved the fundamental theorems of abelian class field theory, as conjectured by Weber and Hilbert. NOETHER ...

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  Number, Theory, Number theory

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