66696 - Algebra Complements

Course Unit Page

Academic Year 2018/2019

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