2022–23–B
Prof. Ido Efrat
Course topics
- Fields: basic properties and examples, the characteristic, prime fields
- Polynomials: irreducibility, the Eisenstein criterion, Gauss’s lemma
- Extensions of fields: the tower property, algebraic and transcendental extensions, adjoining an element to a field
- Ruler and compass constructions
- Algebraic closures: existence and uniqueness
- Splitting fields
- Galois extensions: automorphisms, normality, separability, fixed fields, Galois groups, the fundamental theorem of Galois theory.
- Cyclic extensions
- Solving polynomial equations by radicals: the Galois group of a polynomial, the discriminant, the Cardano-Tartaglia method, solvable groups, Galois theorem
- Roots of unity: cyclotomic fields, the cyclotomic polynomials and their irreducibility
- Finite fields: existence and uniqueness, Galois groups over finite fields, primitive elements