|Elementi di algebra||6||I sem.||Lidia Angeleri, Giovanni Zini|
|Teoria di Galois||3||I sem.||Lidia Angeleri, Giovanni Zini|
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.
Elements of Algebra:
Groups, subgroups, cosets, quotient groups. Solvable groups. Sylow's theorems. 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.
Separable extensions. Galois theory. Theorem of Abel-Ruffini.
Prerequisites: Linear Algebra
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.
|Elementi di algebra||S. Bosch||Algebra||Springer Unitext||2003||978-88-470-0221-0|
|Elementi di algebra||I. N. Herstein||Algebra||Editori Riuniti||2003|