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