A. Agboola

TuTh 2:00pm-3:15pm, HSSB 1215

6724 South Hall, (805) 893-3844

TuTh 11:15am-12:30pm

D. A. Marcus,

A. Frohlich, M. J. Taylor,

The following link will take you to the homework assignments:

There will be no examinations given in this course.

We shall aim to cover the following topics. Additional topics will be covered if time permits.

Basic commutative algebra: Noetherian properties, integrality, rings of integers.

More commutative algebra: Dedekind domains, unique factorisation of ideals, localisation.

Norms, traces and discriminants.

Decomposition of prime ideals in an extension field.

Class numbers and units. Finiteness of the class number: Minkowski bounds. Dirichlet's unit theorem. Explicit calculation of units.

Decomposition of prime ideals revisited: the decomposition group and the inertia group associated to a prime ideal. A nice proof of quadratic reciprocity.