Foundations of Module and Ring Theory

Topological Galois Theory

This book contains below topics, Topological groups and their toposes of continuous actions, A representation theorem, Concrete Galois theories, Other insights from the bridge technique, Examples, The four ways to topological Galois representations.

Author(s): Olivia Caramello

82 Pages

Galois Theory

This book contains below topics, Note to the reader, Overview of Galois theory, Group actions rings and fields, Polynomials, Field extensions, Degree, Splitting fields, Preparation for the fundamental theorem, The fundamental theorem of Galois theory, Solvability by radicals, Finite fields.

Author(s): Tom Leinster

152 Pages

Lecture Notes on Rings and Fields

This note explains the following topics, Numbers, Definitions and first examples, Further axioms for rings, Subrings, Ideals, Quotients of rings, Homomorphisms, Three isomorphism theorems, Prime ideals, Maximal ideals, Divisors, Irreducibles and prime, Euclidean rings, Greatest common divisors again, Some nasty examples, The classification of finite field.

Author(s): J D Mitchell and V Maltcev

50 Pages

Introduction to Groups Rings and Fields by Priestley

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.

Author(s): H. A. Priestley, University of Oxford

41 Pages

Algebra Ring and Field theory by Alireza Salehi Golsefidy

This PDF covers the following topics related to Rings and Fields, A pseudohistorical 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

295 Pages

Foundations of Module and Ring Theory

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 Homfunctor, Notions derived from simple modules, Finiteness conditions in modules, Dual finiteness conditions, Pure sequences and derived notions, Relations between functors and Functor rings.

Author(s): Robert Wisbauer

616 Pages

Ring Theory by wikibook

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.

Author(s): wikibook

NA Pages

Exercises and Solutions In Groups Rings and 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.

Author(s): Mahmut Kuzucuoglu

106 Pages