Università Roma Tre

Groups: symmetric groups, dihedral groups, cyclic and abelian groups. Subgroups. Cosets and Lagrange theorem on the cardinality of a subgroups in finite groups. Homomorphisms. Normal subgroups and quotients. The homomorphism theorems. Action of a group on a set. Orbits and stabilizers. Equation class and its applications (p-groups, center of a group, centralizer of an element). Burnside theorem.
Rings. Domains, fields, skew fields. Subrings and ideals. Homomorphisms: theorems of homomorphism. Prime and maximal ideals. Quotient field of a domain. Divisibility theory: GCD, Bezout identity, PID, ED. Fields: extensions (simple,algebraic and trascendent). Finite fields.

M. Artin, Algebra, BOLLATI BORINGHIERI (1997).