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This note covers rings and ideals, Modules, Monoid algebras and polynomials, Finite fields, Polynomials II, Modules over a PID.
Author(s): Darij Grinberg
493Pages
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
50Pages
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
41Pages
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
295Pages
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
254Pages
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.
Author(s): Robert Wisbauer
616Pages
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
NAPages
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
106Pages
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.
Author(s): F.Beuker
121Pages
This 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.
Author(s): Stevenhagen
84Pages
