SICs and Algebraic Number Theory

Lemmermeyer Algebraic Number Theory

Algebraic Number Theory

These are the notes for a course taught at the University of Michigan in F92 as Math 676. They are available at www.math.lsa.umich.edu/∼jmilne/. Please send comments and corrections to me at [email protected]. v2.01 (August 14, 1996.) First version on the web. v2.10 (August 31, 1998.) Fixed many minor errors; added exercises and index.

Algebraic Number Theory

2 Arithmetic in an algebraic number field 30 2.1 Finitely generated abelian groups . . . . . . . . . . . . . . . . . . 30 2.2 The splitting field and the discriminant . . . . . . . . . . . . . . 31 2.3 Number fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 The ring of integers . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5 Ideals . . . . . . . . . . . . . . ....

Algebraic Number Theory

Algebraic Number Theory