Introduction to Abstract Algebra 2nd Edition by Jonathan D. H. Smith in pdf

 Introduction to Abstract Algebra 2nd Edition by Jonathan D. H. Smith in pdf

this is the book Introduction to Abstract Algebra 2nd Edition in pdf written  by Jonathan D. H. Smith, published by Chapman and Hall/CRC, 2015  of professors of  science faculties  universities  .

   

Information about the book

Language of the book: English language

Book Title: Introduction to Abstract Algebra 2nd Edition

Scriptwriter: by Jonathan D. H. Smith

Year of printing:  Chapman and Hall/CRC, 2015

File Format:PDF

Number of chapters: 11 CHAPTER

Number of pages: 512 pages

File Size: 10,85 MB

Contents

Numbers

Ordering numbers

The Well-Ordering Principle

Divisibility

The Division Algorithm

Greatest common divisors

The Euclidean Algorithm

Primes and irreducibles

The Fundamental Theorem of Arithmetic

Exercises

Study projects

Notes

Functions

Specifying functions

Composite functions

Linear functions

Semigroups of functions

Injectivity and surjectivity

Isomorphisms

Groups of permutations

Exercises

Study projects

Notes

Summary

Equivalence

Kernel and equivalence relations

Equivalence classes

Rational numbers

The First Isomorphism Theorem for Sets

Modular arithmetic

Exercises

Study projects

Notes

Groups and Monoids

Semigroups

Monoids

Groups

Componentwise structure

Powers

Submonoids and subgroups

Cosets

Multiplication tables

Exercises

Study projects

Notes

Homomorphisms

Homomorphisms

Normal subgroups

Quotients

The First Isomorphism Theorem for Groups

The Law of Exponents

Cayley’s Theorem

Exercises

Study projects

Notes

Rings

Rings

Distributivity

Subrings

Ring homomorphisms

Ideals

Quotient rings

Polynomial rings

Substitution

Exercises

Study projects

Notes

Fields

Integral domains

Degrees

Fields

Polynomials over fields

Principal ideal domains

Irreducible polynomials

Lagrange interpolation

Fields of fractions

Exercises

Study projects

Notes

Factorization

Factorization in integral domains

Noetherian domains

Unique factorization domains

Roots of polynomials

Splitting fields

Uniqueness of splitting fields

Structure of finite fields

Galois fields

Exercises

Study projects

Notes

Modules

Endomorphisms

Representing a ring

Modules

Submodules

Direct sums

Free modules

Vector spaces

Abelian groups

Exercises

Study projects

Notes

Group Actions

Actions

Orbits

Transitive actions

Fixed points

Faithful actions

Cores

Alternating groups

Sylow Theorems

Exercises

Study projects

Notes

Quasigroups

Quasigroups

Latin squares

Division

Quasigroup homomorphisms

Quasigroup homotopies

Principal isotopy

Loops

Exercises

Study projects

Note

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