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PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

Index Index

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\(n\)th root of unity, Paragraph
Abelian group, Paragraph
Ackermann’s function, Exercise
Euclidean, Paragraph
Binary operation, Paragraph
Burnside, William, Paragraph
Cancellation law
for groups, Paragraph
Cayley table, Paragraph
Composite integer, Paragraph
Congruence modulo \(n\), Example
Conjugate, complex, Paragraph
De Morgan’s laws
for sets, Theorem
DeMoivre’s Theorem, Theorem
Division algorithm
for integers, Theorem
identity, Item
inverse, Item
order of, Paragraph
Equivalence class, Paragraph
Equivalence relation, Paragraph
Euclidean algorithm, Paragraph
even numbers, Exercise Exercise
bijective, Paragraph
composition of, Paragraph
definition of, Paragraph
domain of, Paragraph
identity, Paragraph
injective, Paragraph
invertible, Paragraph
one-to-one, Paragraph
onto, Paragraph
range of, Paragraph
surjective, Paragraph
Fundamental Theorem
of Arithmetic, Theorem
Galois, Évariste, Paragraph
Generator of a cyclic subgroup, Paragraph
Greatest common divisor
of two integers, Paragraph
abelian, Paragraph
circle, Paragraph
commutative, Paragraph
cyclic, Paragraph
definition of, Paragraph
finite, Paragraph
general linear, Example
infinite, Paragraph
nonabelian, Paragraph
noncommutative, Paragraph
of units, Example
order of, Paragraph
quaternion, Example
special linear, Example
first principle of, Principle
second principle of, Principle
International standard book number, Exercise
Klein, Felix, Paragraph
Lagrange, Joseph-Louis, Paragraph
Lie, Sophus, Paragraph
Linear transformation
definition of, Example
Mapping. See Function
matching bases and subspaces, Exercise
matching derivatives, Exercise
matching US dates, Exercise
similar, Example
Partitions, Paragraph
definition of, Example
Prime integer, Paragraph
prime numbers, Exercise Exercise Exercise
Primitive \(n\)th root of unity, Paragraph
Quaternions, Example
Rigid motion, Paragraph
Sieve of Eratosthenes, Exercise Exercise Exercise Exercise
cyclic, Paragraph
definition of, Paragraph
proper, Paragraph
trivial, Paragraph
Universal Product Code, Exercise
Well-defined map, Paragraph
Well-ordered set, Paragraph