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Abstract Algebra
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This book is on abstract algebra (abstract algebraic systems), an advanced set of topics related to algebra, including groups, rings, ideals, fields, and more. Readers of this book are expected to have read and understood the information presented in the Linear Algebra book, or an equivalent alternative.
Table of Contents
Introduction
/Sets/
/Equivalence relations and congruence classes/
/Functions/
/Binary Operations/
/Linear Algebra/
/Number Theory/
Group Theory
Groups
Subgroups
Cyclic groups
Permutation groups
Homomorphism
Normal subgroups and Quotient groups
Products and Free groups
Group actions on sets
/Composition series/
The Sylow Theorems
Rings
/Rings/
/Ring Homomorphisms/
/Ideals/
/Integral domains/
/Fraction Fields/
/Polynomial Rings/
/Modules/
/Projective line/
Fields
/Fields/
/Factorization/
/Splitting Fields and Algebraic Closures/
/Alphabet field/
/Separability, Normal Extensions/
/Galois Theory/
Vector Spaces
/Vector Spaces/
Algebras
/Algebras/
/Boolean algebra/
/Clifford Algebras/
/Shear and Slope/
/Quaternions/
/2x2 real matrices/
/3x3 real matrices/
/Hypercomplex numbers/
Further abstract algebra
/Category theory/
/Lattice theory/
/Matroids/
/Authors/
Related books
See Subject:Algebra
Information for contributors
/Manual of Style/
Pages in progress
Abstract Algebra/The hierarchy of rings
Abstract Algebra/Rings, ideals, ring homomorphisms
/Sources/
Algebra University level mathematics books
A
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