Algebra (2014/2015)

Course code
Name of lecturers
Lidia Angeleri, Francesca Mantese
Lidia Angeleri
Number of ECTS credits allocated
Academic sector
Language of instruction
I sem. dal Oct 1, 2014 al Jan 30, 2015.

Lesson timetable

I sem.
Day Time Type Place Note
Tuesday 2:30 PM - 4:30 PM lesson Lecture Hall E  
Wednesday 4:30 PM - 6:30 PM lesson Lecture Hall E  
Thursday 1:30 PM - 3:30 PM lesson Lecture Hall E  

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.


Groups, subgroups, cosets, quotient groups. Cyclic groups. The symmetric group. 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. Normal extensions. Separable extensions. Galois theory. Theorem of Abel-Ruffini.

Prerequisites: Linear Algebra

Reference books
Author Title Publisher Year ISBN Note
S. Bosch Algebra Springer Unitext 2003 978-88-470-0221-0
I. N. Herstein Algebra Editori Riuniti 2003

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.

Teaching aids