TOPICS IN ADVANCED ALGEBRA

Degree course: 
Corso di First cycle degree in MATHEMATICS
Academic year when starting the degree: 
2015/2016
Year: 
3
Academic year in which the course will be held: 
2017/2018
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
8
Period: 
Second semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

Knowledge of basic algebraic structures and their properties: groups, rings, polynomials, fields. Knowledge of basic results in linear algebra and matrix calculus.

Final Examination: 
Orale

Written examination immediately followed by an oral examination.

Assessment: 
Voto Finale

Knowledge of Galois Theory with applications.

Ruler and compass constructions. Splitting field of a polynomial. Multiple roots. Perfect fields. (20 hours)

The Galois group. The Galois correspondence. Normal and separable extensions of a field. (20 hours)

Finite soluble groups. Simplicity of the alternating group. The criterion for the solubility by radicals of an equation. The Galois group as the permutation group of the roots of a polynomial. General equation of degree n. (20 hours)

Finite fields. (4 hours)

John M. Howie, Field and Galois Theory, Springer

N. Jacobson, Basic Algebra I, Dover

Frontal lectures and guided exercise sessions

For further detail go to the web page of the course.

Professors