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Algebra 3

A.Y. 2024/2025
9
Max ECTS
93
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The course concerns fields theory and Galois theory, with an introduction to Algebraic Number Theory.
Expected learning outcomes
Knowledge of the main results of Galois Theory and some basic notion of Algebraic Number Theory. Ability of computing the lattice of the subfields a field extension, the Galois group of a Galois extension and ability of applying the basic notions of Algebraic Number Theory.

Lesson period: First semester

Lessons timetable

Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi

Exams calendar

Single course

This course can be attended as a single course.

Take a single course
Course syllabus and organization

Single session

Responsible
Venerucci Rodolfo
Lesson period
First semester
Course syllabus
The concept of trascendence and algebraicity over a field. Existence of algebric closures. Separable and Galois extensions. Fundamental theorem of Galois theory. Finite fields. Cyclotomic ancd cyclic extensions. Galois solvability theorem. Introduction to Algebraic Number Theory.
Prerequisites for admission
Basic knowledge of algebra (Algebra 1-2).
Teaching methods
Blackboard lectures and excercises.
Teaching Resources
-F. Andreatta e M. Bertolini, "Appunti di Teoria dei Numeri". Disponibile nella pagina Ariel
- S. Bosch, Algebra, Unitext, Springer
-J. S. Milne, "Fields and Galois Theory", Version 4.61, April 2020. Disponibile alla pagina web: https://www.jmilne.org/math/CourseNotes/FT.pdf.
Assessment methods and Criteria
The final examination consists of a written exam and an oral discussion, to be given in the same session. It is not allowed to use notes, books or calculators. The students, who have passed the midterm, are exempted from the part of the written exam in January or February, concerning the first part of the course.
MAT/02 - ALGEBRA - University credits: 9
Practicals: 48 hours
Lessons: 45 hours
Professors: Andreatta Fabrizio, Venerucci Rodolfo
Shifts:
Turno
Professors: Andreatta Fabrizio, Venerucci Rodolfo
Professor(s)