User:Zarzuelazen/Books/Reality Theory: Algebra&Number Theory

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Reality Theory: Algebra&Number Theory[edit]

0 (number)
1 (number)
2
2 × 2 real matrices
3
4
Abc conjecture
Abelian extension
Abelian group
Absolute difference
Absolute Galois group
Absolute value
Absolute value (algebra)
Abstract algebra
Acyclic orientation
Addition
Additive function
Additive identity
Additive inverse
Additive map
Additive number theory
Adele ring
Adelic algebraic group
Adjacency matrix
Adjoint representation
Adjugate matrix
Affine Lie algebra
Albert algebra
Algebra
Algebra over a field
Algebra representation
Algebraic closure
Algebraic combinatorics
Algebraic connectivity
Algebraic equation
Algebraic expression
Algebraic extension
Algebraic fraction
Algebraic function field
Algebraic graph theory
Algebraic group
Algebraic integer
Algebraic number
Algebraic number field
Algebraic number theory
Algebraic operation
Algebraic structure
Algebraically closed field
Almost prime
Alternating group
Alternating polynomial
Amicable numbers
Anabelian geometry
Analytic number theory
Annihilator (ring theory)
Antihomomorphism
Antiisomorphism
Antilinear map
Antimatroid
Aperiodic semigroup
Apex graph
Arborescence (graph theory)
Arboricity
Archimedean property
Argument of a function
Arithmetic
Arithmetic function
Arithmetic geometry
Arithmetic group
Arithmetic of abelian varieties
Arity
Arthur–Selberg trace formula
Artin reciprocity law
Ascending chain condition
Associated prime
Association scheme
Associative algebra
Augmented matrix
Automatic group
Automatic semigroup
Automorphic form
Automorphism group
Average order of an arithmetic function
Baby monster group
Bareiss algorithm
Basis (linear algebra)
Bass–Serre theory
Bernoulli number
Bernoulli polynomials
Beta skeleton
Bialgebra
Biconnected component
Biconnected graph
Bijective proof
Bilinear form
Bilinear map
Bimodule
Binary matroid
Binary quadratic form
Binomial (polynomial)
Binomial coefficient
Binomial theorem
Bipartite graph
Bipartite hypergraph
Birch and Swinnerton-Dyer conjecture
Birkhoff's representation theorem
Bivector
Block design
Block matrix
Boolean algebra (structure)
Boolean algebras canonically defined
Boolean ring
Brauer group
Brauer's theorem on induced characters
Bézout domain
Bézout's identity
Cage (graph theory)
Cancellation property
Cancelling out
Carmichael function
Carry (arithmetic)
Cartan decomposition
Cartan matrix
Cartan subalgebra
Cartan's criterion
Catalan number
Cauchy–Schwarz inequality
Cayley graph
Cayley table
Cayley's theorem
Cayley–Hamilton theorem
Center (group theory)
Center (ring theory)
Central simple algebra
Centralizer and normalizer
Chain complex
Change of basis
Character (mathematics)
Character table
Character theory
Characteristic (algebra)
Characteristic polynomial
Chebyshev function
Chebyshev polynomials
Cheeger constant (graph theory)
Chief series
Chinese remainder theorem
Chordal graph
Chromatic polynomial
Circle group
Circuit rank
Class field theory
Class formation
Class function (algebra)
Class number formula
Class number problem
Classical group
Classical orthogonal polynomials
Classification of finite simple groups
Clifford algebra
Clique (graph theory)
Clique complex
Closed-form expression
Coalgebra
Coefficient
Coefficient matrix
Cograph
Cohen structure theorem
Cohomological dimension
Collatz conjecture
Combination
Combinatorial design
Combinatorial group theory
Combinatorial principles
Combinatorial species
Combinatorics
Commutative algebra
Commutative ring
Commutator
Comodule
Compact group
Comparability graph
Complement graph
Complemented lattice
Complete bipartite graph
Complete graph
Complete lattice
Completely distributive lattice
Completely multiplicative function
Completing the square
Completion (algebra)
Completion of a ring
Complex conjugate
Complex number
Complexification
Composite number
Composition (combinatorics)
Composition algebra
Composition series
Computable number
Conductor (ring theory)
Congruence of squares
Congruence relation
Congruence subgroup
Conjugacy class
Conjugate transpose
Connected component (graph theory)
Connected dominating set
Connectivity (graph theory)
Constant (mathematics)
Constant function
Constant term
Constructible number
Continued fraction
Conway chained arrow notation
Conway group
Coordinate vector
Coprime integers
Coset
Counting
Covariance and contravariance of vectors
Covering graph
Coxeter group
Cramer's rule
Cross product
Crossing number (graph theory)
Cube (algebra)
Cube root
Cubic function
Cubic graph
Cusp form
Cuspidal representation
Cut (graph theory)
Cycle (graph theory)
Cycle basis
Cycle graph
Cycle index
Cycle rank
Cycle space
Cycles and fixed points
Cyclic group
Cyclic permutation
Cyclotomic field
De Bruijn–Erdős theorem (graph theory)
Dedekind domain
Dedekind eta function
Dedekind zeta function
Definite quadratic form
Definiteness of a matrix
Degenerate bilinear form
Degree (graph theory)
Degree matrix
Degree of a field extension
Degree of a polynomial
Dense graph
Depth (ring theory)
Derangement
Derivation (differential algebra)
Descartes' rule of signs
Determinant
Diagonal matrix
Diagonalizable matrix
Difference of two squares
Difference set
Differential algebra
Dimension (graph theory)
Dimension (vector space)
Dimension of an algebraic variety
Dimension theory (algebra)
Diophantine approximation
Diophantine equation
Diophantine geometry
Direct product
Direct product of groups
Direct sum
Direct sum of modules
Directed acyclic graph
Directed graph
Dirichlet character
Dirichlet eta function
Dirichlet L-function
Dirichlet's approximation theorem
Dirichlet's theorem on arithmetic progressions
Dirichlet's unit theorem
Discrete group
Discrete logarithm
Discriminant
Discriminant of an algebraic number field
Disjoint union of graphs
Distance (graph theory)
Distance-regular graph
Distance-transitive graph
Distributive lattice
Divisibility (ring theory)
Divisibility rule
Division (mathematics)
Division algebra
Division algorithm
Division by zero
Division ring
Divisor
Divisor function
Divisor summatory function
Domain (ring theory)
Dominating set
Dot product
Double counting (proof technique)
Dual graph
Dual matroid
Dual number
Dual quaternion
Dual representation
Dual space
Dual system
Dyadics
Dynkin diagram
Dynkin index
E8 (mathematics)
E8 lattice
Edge and vertex spaces
Edge coloring
Edge contraction
Eigendecomposition of a matrix
Eigenfunction
Eigenvalues and eigenvectors
Eisenstein series
Elementary algebra
Elementary arithmetic
Elementary matrix
Elementary symmetric polynomial
Elliptic curve
Endomorphism ring
Endoscopic group
Enumerative combinatorics
Equation
Equation solving
Equivariant map
Euclid's lemma
Euclid's theorem
Euclidean division
Euclidean vector
Euler product
Euler system
Euler's theorem
Euler's totient function
Eulerian path
Exact sequence
Expander graph
Expander mixing lemma
Explicit formulae (L-function)
Exponential map (Lie theory)
Exponential sum
Exponentiation
Expression (mathematics)
Exterior algebra
F4 (mathematics)
Factorial
Factorization
Factorization of polynomials
Falling and rising factorials
Faltings's theorem
Fermat number
Fermat's Last Theorem
Fermat's little theorem
Field (mathematics)
Field extension
Field of fractions
Field of sets
Field with one element
Filtered algebra
Filtration (mathematics)
Finite field
Finite group
Finite-rank operator
Finitely generated abelian group
Finitely generated group
Finitely generated module
Five lemma
Floor and ceiling functions
Forbidden graph characterization
Formal group law
Four color theorem
Fraction (mathematics)
Fractional ideal
Frame (linear algebra)
Free abelian group
Free algebra
Free group
Free lattice
Free module
Free monoid
Free object
Free product
Frey curve
Frobenius algebra
Frobenius endomorphism
Functional equation
Functional equation (L-function)
Fundamental domain
Fundamental lemma (Langlands program)
Fundamental pair of periods
Fundamental representation
Fundamental theorem of algebra
Fundamental theorem of arithmetic
Fundamental theorem of Galois theory
Galois cohomology
Galois extension
Galois group
Galois module
Galois theory
Gammoid
Gauss sum
Gaussian binomial coefficient
Gaussian period
Gegenbauer polynomials
General linear group
Generalized eigenvector
Generalized inverse
Generalized Kac–Moody algebra
Generalized Riemann hypothesis
Generating primes
Generating set of a group
Generating set of a module
Generator (mathematics)
Genus of a quadratic form
Geometric algebra
Geometric graph theory
Geometric group theory
Geometric invariant theory
Geometric Langlands correspondence
Geometric lattice
Geometry of numbers
Girth (graph theory)
Global dimension
Global field
Goldbach's conjecture
Golomb–Dickman constant
Graded (mathematics)
Graded Lie algebra
Graded poset
Graded ring
Graded vector space
Graph (discrete mathematics)
Graph automorphism
Graph center
Graph coloring
Graph embedding
Graph isomorphism
Graph labeling
Graph minor
Graph of groups
Graph operations
Graph partition
Graph polynomial
Graph product
Graph property
Graph structure theorem
Graph theory
Graphic matroid
Greatest common divisor
Greedoid
Green's relations
Grothendieck group
Group (mathematics)
Group action (mathematics)
Group algebra
Group cohomology
Group extension
Group homomorphism
Group Hopf algebra
Group isomorphism
Group of Lie type
Group representation
Group ring
Group scheme
Group theory
Hadamard matrix
Hadwiger conjecture (graph theory)
Hamiltonian path
Hamiltonian path problem
Hamming scheme
Handshaking lemma
Hardy–Littlewood circle method
Harmonic number
Hasse principle
Hasse's theorem on elliptic curves
Hasse–Weil zeta function
Hecke character
Height function
Hereditary ring
Hermite polynomials
Hermitian matrix
Hilbert's basis theorem
Hilbert's irreducibility theorem
Hilbert's Nullstellensatz
Hilbert's syzygy theorem
HNN extension
Homeomorphism (graph theory)
Homogeneous function
Homogeneous polynomial
Homogeneous space
Homological algebra
Homomorphism
Hopf algebra
Hurwitz polynomial
Hypercomplex number
Hypergraph
Hyperoperation
Hypertree
Ideal (ring theory)
Ideal class group
Ideal number
Idealizer
Idempotent (ring theory)
Identity (mathematics)
Identity element
Identity matrix
Imaginary number
Imaginary unit
Immanant of a matrix
Incidence matrix
Inclusion–exclusion principle
Indecomposable module
Independent set (graph theory)
Indeterminate (variable)
Index of a subgroup
Indifference graph
Induced path
Induced representation
Induced subgraph
Inequality (mathematics)
Inequation
Injective module
Inner product space
Integer
Integer factorization
Integral domain
Integral element
Interior algebra
Interior product
Intersection graph
Interval graph
Invariant (mathematics)
Invariant theory
Inverse element
Inverse semigroup
Inversion (discrete mathematics)
Invertible matrix
Irrational number
Irreducible element
Irreducible fraction
Irreducible polynomial
Irreducible representation
Isotropic quadratic form
Iwasawa theory
J-invariant
Jacobi identity
Jacobi polynomials
Jacobson radical
Johnson scheme
Jordan algebra
Jordan matrix
Jordan normal form
K-edge-connected graph
K-vertex-connected graph
Kac–Moody algebra
Kazhdan–Lusztig polynomial
Kernel (algebra)
Kernel (linear algebra)
Killing form
Kirchhoff's theorem
Knuth's up-arrow notation
Krohn–Rhodes theory
Kronecker product
Krull dimension
Kummer theory
Kuratowski's theorem
König's lemma
Kőnig's theorem (graph theory)
L-function
Lagrange's four-square theorem
Lagrange's theorem (group theory)
Laguerre polynomials
Lah number
Langlands dual group
Langlands group
Langlands program
Laplace expansion
Laplacian matrix
Latin square
Lattice (discrete subgroup)
Lattice (group)
Lattice (order)
Lattice path
Least common multiple
Leech lattice
Legendre polynomials
Lehmer code
Length of a module
Levi graph
Lie algebra
Lie algebra representation
Lie group
Lie group–Lie algebra correspondence
Lie superalgebra
Like terms
Lindelöf hypothesis
Line graph
Linear algebra
Linear algebraic group
Linear combination
Linear equation
Linear form
Linear group
Linear independence
Linear map
Linear span
Linear subspace
Linearity
Linkless embedding
Liouville function
Liouville number
List of simple Lie groups
List of zeta functions
Local class field theory
Local field
Local ring
Local zeta-function
Localization (algebra)
Localization of a module
Localization of a ring
Locally compact group
Locally linear graph
Logarithm
Logarithm of a matrix
Logarithmic integral function
Loop (graph theory)
Lowest common ancestor
Lowest common denominator
Magic square
Magma (algebra)
Magnitude (mathematics)
Main conjecture of Iwasawa theory
Majorization
Matching (graph theory)
Matrix (mathematics)
Matrix addition
Matrix coefficient
Matrix decomposition
Matrix exponential
Matrix function
Matrix group
Matrix multiplication
Matrix norm
Matrix ring
Matroid
Matroid girth
Matroid minor
Matroid partitioning
Matroid rank
Matroid representation
Maximal ideal
Maximal torus
Median graph
Mersenne prime
Mertens function
Method of conditional probabilities
Method of distinguished element
Minimal polynomial (linear algebra)
Minkowski's theorem
Minor (linear algebra)
Mixed graph
Mixed tensor
Modular arithmetic
Modular form
Modular group
Modular lattice
Modular multiplicative inverse
Modular representation theory
Modularity theorem
Module (mathematics)
Module homomorphism
Modulo operation
Monadic Boolean algebra
Monic polynomial
Monoid
Monomial
Monomial ideal
Monster group
Moore–Penrose inverse
Mordell–Weil theorem
Morita equivalence
Multigraph
Multilinear algebra
Multilinear form
Multilinear map
Multipartite graph
Multiplication
Multiplication algorithm
Multiplication of vectors
Multiplication table
Multiplicative function
Multiplicative group
Multiplicative group of integers modulo n
Multiplicative inverse
Multiplicative number theory
Multivector
MV-algebra
Möbius function
Möbius inversion formula
Nakayama's lemma
Natural density
Natural number
Negative number
Neighbourhood (graph theory)
Nielsen transformation
Nilpotent
Nilpotent group
Noetherian ring
Non-abelian class field theory
Non-abelian group
Non-associative algebra
Noncommutative ring
Nondegenerate form
Nonnegative matrix
Norm (mathematics)
Normal extension
Normal matrix
Normal number
Normal subgroup
Normed vector space
Nth root
Null graph
Null vector
Number
Number theory
Octonion
Octonion algebra
One-form
Operand
Operation (mathematics)
Operator norm
Opposite ring
Order (group theory)
Orders of magnitude (numbers)
Ordered field
Orientation (graph theory)
Orientation (vector space)
Oriented matroid
Orthogonal complement
Orthogonal group
Orthogonal matrix
Orthogonal polynomials
Orthogonality
Orthonormal basis
Orthonormality
Outer product
Overdetermined system
P-adic analysis
P-adic Hodge theory
P-adic L-function
P-adic number
P-adic order
Pairing
Parabolic induction
Parity (mathematics)
Parity of a permutation
Partial cube
Partial fraction decomposition
Partial permutation
Partial trace
Partition (number theory)
Partition function (number theory)
Partition matroid
Partition regularity
Pascal's triangle
Path (graph theory)
Path graph
Pathwidth
Penrose graphical notation
Pentation
Percentage
Perfect graph
Perfect graph theorem
Perfect number
Perfectoid space
Permanent (mathematics)
Permutation
Permutation group
Permutation matrix
Permutation pattern
Perron–Frobenius theorem
Petersen family
Petersen graph
Peter–Weyl theorem
Pigeonhole principle
Planar graph
Planar separator theorem
Platonic graph
Poisson algebra
Polar decomposition
Polarization identity
Polyhedral graph
Polynomial
Polynomial expansion
Polynomial greatest common divisor
Polynomial remainder theorem
Polynomial ring
Polytree
Pontryagin duality
Positive-definite matrix
Presentation of a group
Presentation of a monoid
Primality test
Primary decomposition
Primary ideal
Prime element
Prime gap
Prime ideal
Prime number
Prime number theorem
Prime power
Prime-counting function
Primitive root modulo n
Principal ideal
Principal ideal domain
Probabilistic method
Probable prime
Product (mathematics)
Product ring
Profinite group
Projection (linear algebra)
Projective linear group
Projective module
Projective orthogonal group
Projective representation
Proportionality (mathematics)
Prüfer domain
Pseudoscalar
Pseudovector
Pólya enumeration theorem
Q-analog
Q-Pochhammer symbol
Quadratic equation
Quadratic field
Quadratic form
Quadratic formula
Quadratic function
Quadratic integer
Quadratic reciprocity
Quadratic residue
Quantale
Quantum group
Quartic function
Quasigroup
Quaternion
Quaternion algebra
Quiver (mathematics)
Quotient
Quotient algebra
Quotient graph
Quotient group
Quotient ring
Quotient space (linear algebra)
Radical of a module
Radical of an ideal
Radical of an integer
Raising and lowering indices
Ramsey theory
Ramsey's theorem
Rank (graph theory)
Rank (linear algebra)
Rank of a group
Rank of an abelian group
Ratio
Rational function
Rational number
Rational point
Rayleigh quotient
Reachability
Real form (Lie theory)
Real number
Real representation
Real structure
Reciprocity law
Reduced residue system
Reductive group
Regular graph
Regular matroid
Regular prime
Regular representation
Regular semigroup
Relative change and difference
Remainder
Representation of a Lie group
Representation of a Lie superalgebra
Representation theory
Representation theory of finite groups
Representation theory of the symmetric group
Residually finite group
Residuated lattice
Residue field
Resolution (algebra)
Resultant
Ribet's theorem
Riemann hypothesis
Riemann zeta function
Rigid analytic space
Ring (mathematics)
Ring homomorphism
Ring of integers
Ring of mixed characteristic
Ring of symmetric functions
Ring theory
Rng (algebra)
Robertson–Seymour theorem
Root of unity
Root system
Rotation matrix
Roth's theorem
Rouché–Capelli theorem
Routh–Hurwitz theorem
Row and column spaces
Row and column vectors
Rule of product
Rule of sum
Scalar (mathematics)
Scalar multiplication
Scalar projection
Schmidt decomposition
Schreier's lemma
Schur polynomial
Selberg trace formula
Self-complementary graph
Semi-simplicity
Semidirect product
Semifield
Semigroup
Semigroup action
Semigroup with involution
Semilattice
Semimodular lattice
Semiprime
Semiring
Semisimple algebra
Semisimple Lie algebra
Semisimple module
Separable extension
Series-parallel graph
Sesquilinear form
Seven Bridges of Königsberg
Shear matrix
Sieve theory
Sign (mathematics)
Signed graph
Simple algebra
Simple group
Simple Lie group
Simple module
Singly and doubly even
Singular value decomposition
Skew partition
Skew-symmetric graph
Skew-symmetric matrix
Skewes's number
Snake lemma
Solution set
Solvable group
Spanning tree
Special linear group
Special unitary group
Spectral graph theory
Spectral sequence
Spin group
Spin representation
Split graph
Split-complex number
Split-octonion
Split-quaternion
Sporadic group
Square (algebra)
Square-free integer
Square matrix
Square number
Square root
Square root of 2
Square root of a matrix
Stable polynomial
Standard basis
Stanley–Reisner ring
*-algebra
Stirling number
Strong perfect graph theorem
Strongly connected component
Strongly regular graph
Structure constants
Structure theorem for finitely generated modules over a principal ideal domain
Subalgebra
Subdirect product
Subdirectly irreducible algebra
Subgroup
Subgroup series
Subring
Substitution (algebra)
Subtraction
Summation
Super vector space
Superalgebra
Supercommutative algebra
Supergroup (physics)
Supermodule
Superpattern
Superpermutation
Sylow theorems
Symbolic method (combinatorics)
Symmetric algebra
Symmetric bilinear form
Symmetric function
Symmetric graph
Symmetric group
Symmetric matrix
Symmetric polynomial
Symmetrization
Symplectic group
Symplectic matrix
Symplectic vector space
System of linear equations
System of polynomial equations
Table of Lie groups
Tate cohomology group
Tate module
Tensor algebra
Tensor contraction
Tensor product
Tensor product of representations
Tensor rank decomposition
Tetration
Topological algebra
Topological graph
Topological graph theory
Topological group
Topological ring
Torsion (algebra)
Total ring of fractions
Totally positive matrix
Tournament (graph theory)
Trace (linear algebra)
Trace diagram
Transcendental number
Transcendental number theory
Transformation matrix
Transformation semigroup
Transitive reduction
Transpose
Transpose of a linear map
Transversal (combinatorics)
Tree (graph theory)
Tree decomposition
Tree-depth
Treewidth
Triangle-free graph
Triangular matrix
Triangular number
Trinomial
Triple product
Triple system
Trivial representation
Trémaux tree
Tutte polynomial
Twelvefold way
Twin prime
Unary operation
Underdetermined system
Uniform matroid
Unimodular lattice
Unique factorization domain
Unit (ring theory)
Unit distance graph
Unit vector
Unitary group
Unitary matrix
Unitary representation
Unitary transformation
Universal algebra
Universal embedding theorem
Universal enveloping algebra
Valuation (algebra)
Variable (mathematics)
Variety (universal algebra)
Variety of finite semigroups
Vector (mathematics and physics)
Vector projection
Vector space
Vertex (graph theory)
Vertex cover
Vertex-transitive graph
Von Mangoldt function
Wagner's theorem
Waring's problem
Weight (representation theory)
Weil conjectures
Weil group
Weyl algebra
Weyl character formula
Weyl group
Wheel theory
Witt group
Witt vector
Witt's theorem
Word (group theory)
Wreath product
Young tableau
Zero divisor
Zero element
Zero matrix
Zero of a function
Zero ring