# SUPERIOR ALGEBRA

**Academic Year 2023/2024**- Teacher:

**Marco D'ANNA**

## Expected Learning Outcomes

## Course Structure

In the course the will be lectures and exercises, given at the blackboard by the lecturer, and class exercises. Ussually the lecturer alternates exercises and theoretical parts in the same day. As for class exercises, the lecturer gives some exercises to the students, that have to try to solve them working in small groups; the lecturer helps the students to find the proper way to appoach the exercises.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

## Required Prerequisites

## Detailed Course Content

Norms, traces and discriminants.

Quadratic and cyclotomic extensions.

Dedekind domains.

Factorization of prime ideals in extensions.

The ideal class group.

The Dirichlet unit theorem.

If there will be time other extra contents (e.g. factorization of prime ideals in Galois extensions) will be added.

## Textbook Information

1. Notes given by the lecturer.

2. Marcus D.A, Number Fields, Springer 1977

3. Stewart I and Tall D, Algebraic number theory, Chapman and Hall 1987

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Recap on integral extensions | 1 |

2 | Quadratic and cyclotomic extensions | 1 |

3 | Norms, traces and discriminants. | 1 |

4 | Dedekind domains | 1 |

5 | Factorization of prime ideals in extensions | 1 |

6 | The ideal class group | 1 |

7 | The Dirichlet unit theorem | 1 |