Università Roma Tre

Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. Actions of a group on a set. Orbits and stabilizers theorems. Sylow theorems and their applications. Rings: Rings, domains and fields. Sub-rings, subfields and ideals. Homomorphisms. Quotient rings. Homomorphism theorems. Prime and maximum ideals. The quotient field of a domain. Divisibility in a domain. Fields: Field extensions (simple, algebraic and transcendental). Splitting field of a polynomial. Finite fields.

Lecture notes