|Teoria||3||I semestre||Lidia Angeleri|
|Esercitazioni||2||I semestre||Lidia Angeleri|
|Esercitazioni||1||I semestre||Dirk Kussin|
|Teoria||Tuesday||2:30 PM - 4:30 PM||lesson||Lecture Hall E|
|Teoria||Thursday||1:30 PM - 3:30 PM||lesson||Lecture Hall E|
|Esercitazioni||Wednesday||4:30 PM - 6:30 PM||practice session||Lecture Hall E|
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 group. 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
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.
|Title||Format (Language, Size, Publication date)|
|Filo rosso||pdf (it, 532 KB, 09/01/12)|
|Presentazione corso||pdf (it, 185 KB, 02/10/11)|
|Prove scritte appelli 1 e 2||pdf (it, 97 KB, 22/02/12)|
|Prove scritte appelli 1 e 2 - soluzioni||pdf (it, 5700 KB, 22/02/12)|