Algebra (2020/2021)

Course code
Enrico Gregorio
Other available courses
Teaching is organised as follows:
Unit Credits Academic sector Period Academic staff
ELEMENTI DI ALGEBRA 6 MAT/02-ALGEBRA II semestre Ancora Da Definire
Enrico Gregorio
TEORIA DI GALOIS 3 MAT/02-ALGEBRA II semestre Ancora Da Definire
Enrico Gregorio

Learning outcomes

The course provides an introduction to modern algebra. After presenting and discussing the main algebraic structures (groups, rings, fields), the focus is on Galois theory. Also some applications are discussed, in particular results on solvability of polynomial equations by radicals. At the end of the course the student will be expected to demonstrate that s/he has attained adequate skills in synthesis and abstraction, as well as the ability to recognize and produce rigorous proofs and to formalize and solve moderately difficult problems related to the topics of the course.


MM: Elementi di algebra teoria
Groups, subgroups, cosets, quotient groups. Cyclic groups. The symmetric group. Sylow's Theorems. Solvable groups. Rings. Ideals. Homomorphisms. Principal ideal domains. Unique factorization domains. Euclidean rings. The ring of polynomials. Fields. Algebraic field extensions. The splitting field of a polynomial. Finite fields. Constructions with ruler and compass.
MM: Elementi di algebra esercitazioni

MM: Teoria di Galois teoria
Normal extensions. Separable extensions. Galois theory. Theorem of Abel-Ruffini.
MM: Teoria di Galois esercitazioni

Assessment methods and criteria

The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained for the homework and/or by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination.

Reference books
Author Title Publisher Year ISBN Note
I. N. Herstein Algebra Editori Riuniti 2003
Sigfried Bosch Algebraic Geometry and Commutative Algebra Springer 2013