This
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
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.
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.
Aim of
this book is to help the students by giving them some exercises and get them
familiar with some solutions. Some of the solutions here are very short and in
the form of a hint. Topics covered includes: Sets, Integers, Functions, Groups,
Rings and Fields.