A
abelian (group)
act, action
addition
(modulo an integer)
addition
(of polynomials)
addition
(modulo a polynomial)
addition
(ring)
additive group
(of a ring)
algebraic (number)
algebraic (over a field)
alternating group
automorphism
automorphism group
a-ary number system
a-ary representation
B
basis
(of a permutation group)
basis
(of a vector space)
bijection, bijective
map
bijection, bijective
map
binomium
Bubble Sort
binary code
binary operation
binary operation
C
cancellation law (domains)
cancellation law (monoids)
Cartesian product
centralizer (subgroup)
centralizer
center
center
characteristic (field)
characteristic polynomial
(of a matrix)
check polynomial
Chinese Remainder Theorem
Chinese Remainder Theorem (see Exercise 9)
closed
coefficient
coefficient ring
code
code generated by a polynomial
code words
coding theory
common multiple (integers)
common multiple (polynomials)
common divisor
(integers)
common divisor
(polynomials)
commutative
(binary operation)
commutative (group)
commutative (ring)
complement
complex numbers
composition
composition
connected (graph)
congruent modulo a number
congruent modulo a polynomial
congruent modulo an ideal
conjugacy class
conjugation
conjugation representation
constant
coset
cycle (permutation)
cycle (graph)
cycle notation
cycle structure
cyclic code
cyclic group
cyclic monoid
D
decoding number
degree (polynomial)
degree (representation)
denominator
derivative
detection pattern
dihedral group
dihedral group
direct product (monoid)
direct product (ring)
distance
divisible
(integers)
divisible
(polynomials)
division with remainder (integers)
division with remainder
(polynomials)
divisor (integers)
divisor (polynomials)
divisor (ring)
disjoint cycles form (permutation)
disjoint cycles notation (permutation)
E
encoding number
equivalence class
equivalence relation
equivalence (congruence modulo an ideal)
equivalence (congruence modulo an integer)
equivalence (congruence modulo a polynomial)
equivalence
(congruence modulo a subgroup)
equivalence
(in the same coset)
equivalence
(equal as quotient)
equivalence
(in the same orbit)
Eratosthenes' sieve
error-correcting code
Euclid's algorithm (integers)
Euclid's algorithm (polynomials)
Euler indicator
even
extended Euclidean algorithm (integers)
extended Euclidean algorithm (polynomials)
F
factor (integers)
factor (polynomials)
factorization (integers)
factorization (polynomials)
Fano plane
Fermat's little
theorem
Fermat's conjecture on primes (Exercise 10)
Fermat little
theorem (reformulated)
Fermat little
theorem (for arbitrary finite fields)
field (informal)
field (formal)
finite field
field of fractions
first isomorphism theorem (group)
first isomorphism theorem (ring)
fix
fixed points
free monoid
free semi-group
fundamental theorem of algebra
G
Gaussian integers
Gaussian numbers
gcd (integers)
gcd (polynomials)
general linear group
generated (monoid)
generated (group)
generated (field)
generated (ideals)
generated (code)
graph
greatest common divisor
(integers)
greatest common divisor
(polynomials)
group
I
ideal
identified
identity element
identity map
image
indeterminate (polynomial)
indeterminate (over a ring)
index
induced monoid
injective
integer
inverse (modulo an integer)
inverse (modulo a polynomial)
inverse (ring)
inverse image
invertible (modulo an integer)
invertible (modulo a polynomial)
invertible (ring)
irreducible (polynomial)
isomorphism (monoid)
isomorphism (group)
isomorphism (ring)
isomorphism (graph)
isomorphism theorem (group)
isomorphism theorem (ring)
J
K
kernel (group morphism)
kernel (ring morphism)
Klein's Vierergroup (Exercise 14)
Kronecker product
L
Lagrange's theorem
lcm (integers)
lcm (polynomials)
leading coefficient
leading term
least common multiple (integers)
least common multiple (polynomials)
left coset
left regular representation
linear code
linear congruence
linear factor
linear polynomial
M
matrix
Mersenne prime
minimal distance
minimal polynomial
mod (integer)
mod (polynomial)
modulus
monic
monoid
monoid induced by
monoid generated by
monomial
morphism (monoid)
morphism (graph)
morphism (group)
morphism (ring)
morphism (field)
multiple (integers)
multiple (polynomials)
multiplication
(modulo an integer)
multiplication
(of polynomials)
multiplication
(modulo a polynomial)
multiplication
(of permutations)
multiplication
(semi-group)
multiplication
(group)
multiplication
(ring)
multiplicative inverse
O
odd
opposite (polynomial)
optimal (detection pattern)
opposite (in a ring)
order
(integer mod n)
order
(of a monoid)
order
(of a group)
order
(of a matrix)
P
permutation
permutation matrix
permutation group
permutation representation
Petersen graph
polynomial
polynomial (over a ring)
polynomial ring
polynomial function
prime (number)
prime factor
primitive element
primitive
product
(modulo an integer)
product
(of polynomials)
product
(modulo a polynomial)
product
(of permutations)
product
(semi-group)
product
(group)
product
(ring)
proper
Q
quaternion group
quaternions (ring)
quotient (integers)
quotient (polynomials)
quotient ring
(polynomials)
quotient ring
R
radar
rational functions field
register
regular representation
relatively prime (integers)
relatively prime (polynomials)
representative
residue class (polynomials)
residue class ring (ring)
right coset
right regular representation
ring
RSA cryptosystem
S
Schreier element
Schreier tree
set
shift polynomial
shift register
sign
special linear group
stabilize, stabilizer
structure
subfield (Exercise 19)
subfield
subgroup
submonoid
subring
sum
(modulo an integer)
sum
(of polynomials)
sum
(modulo a polynomial)
sum
(ring)
support
surjective
Sylow subgroup
symmetric group
U
unique factorization (numbers)
unique factorization (polynomials)
unit (ring)
unit (semi-group)
unity, unit element
W
X
Y