Abstract Algebra

Course content

Groups. Isomorphism theorems, direct pro-ducts. Groups acting on sets. Class equation. Statements of Sylow theorems and the F.T. on finite abelian groups. Rings, isomorphism theorems. Prime and maximal ideals. Integral domains, field of fractions. Euclidean domains, PIDs, UFDs. Polynomials, polynomials in several variables. Field extensions. Impossibility of certain geometric constructions. Finite fields.