This wikibook explains ring theory. Topics
covered includes: Rings, Properties of rings, Integral domains and Fields,
Subrings, Idempotent and Nilpotent elements, Characteristic of a ring,
Ideals in a ring, Simple ring, Homomorphisms, Principal Ideal Domains,
Euclidean domains, Polynomial rings, Unique Factorization domain, Extension
fields.

On the one hand this
book intends to provide an introduction to module theory and the related
part of ring theory. Topics covered includes: Elementary properties of
rings, Module categories, Modules characterized by the Hom-functor, Notions
derived from simple modules, Finiteness conditions in modules, Dual
finiteness conditions, Pure sequences and derived notions, Relations between
functors and Functor rings.

This wikibook explains ring theory. Topics
covered includes: Rings, Properties of rings, Integral domains and Fields,
Subrings, Idempotent and Nilpotent elements, Characteristic of a ring,
Ideals in a ring, Simple ring, Homomorphisms, Principal Ideal Domains,
Euclidean domains, Polynomial rings, Unique Factorization domain, Extension
fields.

This note covers the following topics:
Rings: Definition, examples and elementary properties, Ideals and ring
homomorphisms, Polynomials, unique factorisation, Factorisation of polynomials,
Prime and maximal ideals, Fields, Motivatie Galoistheorie, Splitting fields and
Galois groups, The Main Theorem of Galois theory, Solving equation and Finite
fields.