Caterina Dolcini: Fundamental concepts in ring theory. Diplom thesis, Ferrara 1988. Original title: Concetti fondamentali della teoria degli anelli.

RINGS AND MODULES Introduction to rings If A is integer, every finite subgroup of A* is cyclic Modules on a ring Homomorphisms of modules Chain conditions The theorem of Jordan-Hölder Direct sums and direct products of modules Direct summands and projectors Exact sequences Split exact sequences Projective modules Injective modules The role of idempotents Semisimple modules The Krull-Remak-Schmidt theorem Direct products of rings The radical of a module The radical of a ring Local rings The structure theorem for finite commutative rings Idempotents in a finite ring The invertible elements of a finite commutative ring CYCLOTOMIC POLYNOMIALS AND FINITE FIELDS Summary of Galois theory Roots of unity and cyclotomic polynomials The Galois group of a cyclotomic extension Finite fields The finite field with 9 elements Wedderburn's theorem REFERENCES