Algebra Ring and Field theory by Alireza Salehi Golsefidy
Algebra Ring and Field theory by Alireza Salehi Golsefidy
Algebra Ring and Field theory by Alireza Salehi Golsefidy
This PDF covers the following topics related to Rings and
Fields : A pseudo-historical note, More on subrings and ring
homomorphisms, The evaluation or the substitution map, Defining fractions, Using
the universal property of the field of fractions, An application of the first
isomorphism theorem, The factor theorem and the generalized factor theorems,
Gaussian integers, Irreducibility and zeros of polynomials,
Content of a polynomial with rational coefficients, An example on the mod
irreducibility criterion, Factorization: uniqueness, and prime elements, Ring of
integer polynomials is a UFD, Greatest common divisor for UFDs, Extension of
isomorphisms to splitting fields, Finite fields, etc.
Author(s): Alireza Salehi
Golsefidy, University of California San Diego
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 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.
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.