The aim of the course is to introduce students to the basic notions of Galois theory and commutative algebra. Tools from differnt areas of mathematics (e.g. topology) will be used in order to make students acquainted with an interdisciplinary approach to mathematics.
Prerequisites
Algebra I e II
Teaching Methods
Lectures
Type of Assessment
Oral exam. The student is supposed to show to have understood the topics discussed and should be able to use them to work out some examples.
Course program
Cyclotomic fields. Artin's theorem. Dedekind's Lemma. Kummer's theorem. Solvable groups and composition series. Radical extentions. oup. Radicals in rings (nilpotent radical, Jacobson's radical). F.g. modules. Noetherian and artinian rings and modules. Primary decomposition. Localization. Dedekind rings.