Academic Year 2018/2019
- Docente: Marta Morigi
- Credits: 6
- SSD: MAT/02
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Course contents
Galois Theory:
Splitting field of a polynomial. Symmetric functions. Normal fields extensions. Separable fields extensions. The primitive element theorem. Galois extensions. The Galois group of a field extension. The Galois correspondence. The Galois group of a polynomial. The discriminant of a polynomial.
Commutative algebra;
Commutative rings. Prime and maximal ideals. Modules: basic definitions. Direct product and sum of modules. Free modules. Noetherian and artinian modules. Noetherian rings. Hilbert basis theorem. Finitely generated modules and thier presentation. Definition of algebra. Modules over euclidean rings and PID. Decomposition of a module over an euclidean ring and its consequences. Canonical forms of endomorphisms. Tensor product of modules.
Readings/Bibliography
.S. Milne "Fields and Galois Theory"
Cox "Galois Theory"
M. Atyiah, I. G. Macdonald "Commutative algebra"
E. Artin, “Algebra”
S. Lang, “Algebra”
Assessment methods
Oral examination.
Links to further information
http://www.dm.unibo.it/~mmorigi/compl_alg/complalg16-17.html
Office hours
See the website of Marta Morigi