Syllabus
1. Fractional ideals of Dedekind domains, absolute norm of ideals, the finiteness of class groups.
2. Lattices. Blichfeldt's lemma.
3. Units of rings of algebraic integers, Dirichlet's Unit Theorem.
4. Quadratic and cubic fields, selected Diophantine equations.
Annotation
A recommended elective course for bachelor's program in Information security. The lecture introduces notions of algebraic number theory.
Beside the theory of Dedekind domains, which will be deepened and illustrated, the lecture will be focused on number fields, ideal class groups and quadratic fields.