Algebra (2009/2010)

Course code
4S00022
Name of lecturer
Lidia Angeleri
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Location
VERONA
Period
1st Semester dal Oct 1, 2009 al Jan 31, 2010.
Web page
http://profs.sci.univr.it/~angeleri/lehre.html

Lesson timetable

1st Semester
Day Time Type Place Note
Tuesday 2:30 PM - 4:30 PM lesson Lecture Hall E  
Wednesday 1:30 PM - 2:30 PM lesson Lecture Hall E  
Wednesday 4:30 PM - 6:30 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, 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 and an oral examination. Only students who have passed the written exam will be admitted to the oral examination.

Teaching aids

Documents