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, 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
|S. Bosch||Algebra||Springer Unitext||2003||978-88-470-0221-0|
|I. N. Herstein||Algebra||Editori Riuniti||2003|
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.