PDF covers the following topics related to Rings and Fields : A brief overview,
An introduction to Rings, Integral Domains and Fields, Homorphisms, ideals and
quotient rings, Prime ideals, maximal ideals, and fields of quotients, Euclidean
Domains, Factorisation in polynomial rings, Vector spaces, Extension fields,
Straight-edge and Compasses constructions.
Author(s): Laurent W. Marcoux, University of Waterloo
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 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
note covers the following topics: Introduction to number rings, Ideal
arithmetic, Explicit ideal factorization, Linear algebra for number rings,
Geometry of numbers, Zeta functions, Computing units and class groups, Galois
theory for number fields.