# IndexIndex

$G$-equivalent
$G$-set
$n$th root of unity
Abel, Niels Henrik
Abelian group
Ackermann's function
Algebraic closure
Algebraic extension
Algebraic number
Algorithm
division
Euclidean
Ascending chain condition
Associate elements
Atom
Automorphism
inner
Basis of a lattice
Bieberbach, L.
Binary operation
Binary symmetric channel
Boole, George
Boolean algebra
atom in a
definition of
finite
isomorphism
Boolean function
Burnside's Counting Theorem
Burnside, William
Cancellation law
for groups
for integral domains
Cardano, Gerolamo
Carmichael numbers
Cauchy's Theorem
Cauchy, Augustin-Louis
Cayley table
Cayley's Theorem
Cayley, Arthur
Centralizer
of a subgroup
Characteristic of a ring
Chinese Remainder Theorem
for integers
Cipher
Ciphertext
Circuit
parallel
series
series-parallel
Class equation
Code
BCH
cyclic
group
linear
minimum distance of
polynomial
Commutative diagrams
Commutative rings
Composite integer
Composition series
Congruence modulo $n$
Conjugacy classes
Conjugate elements
Conjugate, complex
Conjugation
Constructible number
Correspondence Theorem
for groups
for rings
Coset
left
representative
right
Coset decoding
Cryptanalysis
Cryptosystem
affine
definition of
monoalphabetic
polyalphabetic
private key
public key
RSA
single key
Cycle
definition of
disjoint
De Morgan's laws
for Boolean algebras, Item
for sets
De Morgan, Augustus
Decoding table
Deligne, Pierre
DeMoivre's Theorem
Derivative
Determinant, Vandermonde
Dickson, L. E.
Diffie, W.
Direct product of groups
external
internal
Discriminant
of the cubic equation
Division algorithm
for integers
for polynomials
Division ring
Domain
Euclidean
principal ideal
unique factorization
Doubling the cube
Eisenstein's Criterion
Element
associate
identity, Item
inverse, Item
irreducible
order of
prime
primitive
transcendental
Equivalence class
Equivalence relation
Euclidean algorithm
Euclidean domain
Euclidean group
Euclidean inner product
Euclidean valuation
Euler $\phi$-function
Euler, Leonhard
Extension
algebraic
field
finite
normal
separable
simple
External direct product
Faltings, Gerd
Feit, W.
Fermat's factorizationalgorithm
Fermat's Little Theorem
Fermat, Pierre de
Ferrari, Ludovico
Ferro, Scipione del
Field
algebraically closed
base
extension
fixed
Galois
of fractions
of quotients
splitting
Finitely generated group
Fior, Antonio
First Isomorphism Theorem
for groups
for rings
Fixed point set
Freshman's Dream
Function
bijective
Boolean
composition of
definition of
domain of
identity
injective
invertible
one-to-one
onto
range of
surjective
switching
Fundamental Theorem
of Algebra
of Arithmetic
of Finite Abelian Groups
Fundamental Theorem of Galois Theory
Galois field
Galois group
Galois, Évariste
Gauss's Lemma
Gauss, Karl Friedrich
Gaussian integers
Generator of a cyclic subgroup
Generators for a group
Glide reflection
Gorenstein, Daniel
Greatest common divisor
of two integers
of two polynomials
Greatest lower bound
Greiss, R.
Grothendieck, Alexander
Group
abelian
action
alternating
center of
circle
commutative
cyclic
definition of
dihedral
Euclidean
factor
finite
finitely generated
Galois
general linear
generators of
homomorphism of
infinite
isomorphic
isomorphism of
nonabelian
noncommutative
of units
order of
orthogonal
permutation
point
quaternion
quotient
simple
solvable
space
special linear
special orthogonal
symmetric
symmetry
Group!$p$-group
Gödel, Kurt
Hamming distance
Hamming, R.
Hellman, M.
Hilbert, David
Homomorphic image
Homomorphism
canonical
evaluation
kernel of a group
kernel of a ring
natural
of groups
ring
Ideal
definition of
maximal
one-sided
prime
principal
trivial
two-sided
Indeterminate
Index of a subgroup
Induction
first principle of
second principle of
Infimum
Inner product
Integral domain
Internal direct product
International standard book number
Irreducible element
Irreducible polynomial
Isometry
Isomorphism
of Boolean algebras
of groups
ring
Join
Jordan, C.
Jordan-Hölder Theorem
Kernel
of a group homomorphism
of a ring homomorphism
Key
definition of
private
public
single
Klein, Felix
Kronecker delta
Kronecker, Leopold
Kummer, Ernst
Lagrange's Theorem
Lagrange, Joseph-Louis
Laplace, Pierre-Simon
Lattice
completed
definition of
distributive
Lattice of points
Lattices, Principle of Duality for
Least upper bound
Left regular representation
Lie, Sophus
Linear combination
Linear dependence
Linear independence
Linear map
Linear transformation
definition of
Lower bound
Mapping, see Function
Matrix
distance-preserving
generator
inner product-preserving
invertible
length-preserving
nonsingular
null space of
orthogonal
parity-check
similar
unimodular
Matrix, Vandermonde
Maximal ideal
Maximum-likelihood decoding
Meet
Minimal generator polynomial
Minimal polynomial
Minkowski, Hermann
Monic polynomial
Mordell-Weil conjecture
Multiplicity of a root
Noether, A. Emmy
Noether, Max
Normal extension
Normal series of a group
Normal subgroup
Normalizer
Null space
of a matrix
Odd Order Theorem
Orbit
Orthogonal group
Orthogonal matrix
Orthonormal set
Partial order
Partially ordered set
Partitions
Permutation
definition of
even
odd
Permutation group
Plaintext
Polynomial
code
content of
definition of
degree of
error
error-locator
greatest common divisor of
irreducible
minimal
minimal generator
monic
primitive
root of
separable
zero of
Polynomial separable
Polynomial!in $n$ indeterminates
Poset
definition of
largest element in
smallest element in
Power set
Prime element
Prime ideal
Prime integer
Primitive $n$th root of unity
Primitive element
Primitive Element Theorem
Primitive polynomial
Principal ideal
Principal ideal domain (PID)
Principal series
Pseudoprime
Quaternions
Resolvent cubic equation
Rigid motion
Ring
characteristic of
commutative
definition of
division
factor
homomorphism
isomorphism
Noetherian
quotient
with identity
with unity
Rivest, R.
RSA cryptosystem
Ruffini, P.
Russell, Bertrand
Scalar product
Second Isomorphism Theorem
for groups
for rings
Shamir, A.
Shannon, C..
Sieve of Eratosthenes
Simple extension
Simple group
Simple root
Spanning set
Splitting field
Squaring the circle is impossible
Standard decoding
Subgroup
centralizer
commutator
cyclic
definition of
index of
isotropy
normal
normalizer of
proper
stabilizer
Sylow$p$-subgroup
translation
trivial
Subgroup!$p$-subgroup
Subnormal series of a group
Subring
Supremum
Switch
closed
definition of
open
Switching function
Sylow $p$-subgroup
Sylow, Ludvig
Syndrome of a code
Tartaglia
Third Isomorphism Theorem
for groups
for rings
Thompson, J.
Transcendental element
Transcendental number
Transposition
Trisection of an angle
Unique factorization domain (UFD)
Unit
Universal Product Code
Upper bound
Vandermonde determinant
Vandermonde matrix
Vector space
basis of
definition of
dimension of
subspace of
Weight of a codeword
Weil, André
Well-defined map
Well-ordered set