This PDF covers the following topics related to Groups, Rings and Fields
: Familiar algebraic systems: review and a look ahead, Binary operations, and a
first look at groups, Interlude: properties of the natural numbers, Integers,
Polynomials, Equivalence relations, and modular arithmetic.
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