# Algebra (2015/2016)

Course code
4S00022
Credits
6
Coordinator
Lidia Angeleri
MAT/02 - ALGEBRA
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 4 I semestre Lidia Angeleri
Teoria - esercitazioni 2 I semestre Jorge Nuno Dos Santos Vitoria

### Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria Tuesday 10:30 AM - 12:30 PM lesson Lecture Hall H
Teoria Thursday 1:30 PM - 3:30 PM lesson Lecture Hall E
Teoria - esercitazioni Tuesday 3:30 PM - 5:30 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.

### Syllabus

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

### 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.

 Activity Author Title Publisher Year ISBN Note Teoria S. Bosch Algebra Springer Unitext 2003 978-88-470-0221-0 Teoria I. N. Herstein Algebra Editori Riuniti 2003
 Title Format (Language, Size, Publication date) Appello 4 del 13/9/2016 pdf (it, 117 KB, 15/09/16) Filo rosso pdf (it, 505 KB, 14/01/16) PRESENTAZIONE CORSO pdf (it, 201 KB, 02/10/15) Primo appello pdf (it, 104 KB, 13/02/16) Esercizi - Foglio 1 pdf (it, 74 KB, 07/10/15) Esercizi - Foglio 2 - corretto pdf (it, 73 KB, 19/10/15) Esercizi - Foglio 3 pdf (it, 67 KB, 20/10/15) Esercizi - Foglio 4 pdf (it, 71 KB, 28/10/15) Esercizi - Foglio 5 pdf (it, 75 KB, 03/11/15) Esercizi - Foglio 6 pdf (it, 70 KB, 16/11/15) Esercizi - Foglio 7 - corretto pdf (it, 89 KB, 21/11/15) Esercizi - Foglio 8 - corretto pdf (it, 83 KB, 08/01/16) Esercizi - Foglio 9 pdf (it, 91 KB, 12/01/16)