Every idea

Ideas 8851–9000 of 10181.

Name	Kind	Subject
Borel–Moore homology	Concept	Algebraic topology
Compositum of fields	Concept	Field theory and polynomials
Associative quotient of a magma	Concept	Group theory and generalizations
Maximal compact subgroup	Concept	Topological groups, Lie groups
Mean curvature	Definition	Differential geometry
Triangulated category	Concept	Category theory; homological algebra
Topological vector space	Concept	Functional analysis
Rate of convergence	Definition	Sequences, series, summability
Dimension of a polynomial ring	Theorem	Commutative algebra
Isomorphism of topological groups	Concept	Topological groups, Lie groups
Sylvester–Gallai theorem	Theorem	Convex and discrete geometry
Reidemeister's theorem	Theorem	Manifolds and cell complexes
Differential field	Definition	Field theory and polynomials
Primal algebra	Definition	General algebraic systems
Omega-complete partial order	Concept	Order, lattices, ordered algebraic structures
4-manifold	Definition	Manifolds and cell complexes
Nerve theorem	Theorem	Algebraic topology
The alternating group A3 is normal in S3	Example	Group theory and generalizations
Gelfand's spectral radius formula	Theorem	Functional analysis
Doléans-Dade exponential	Definition	Probability theory and stochastic processes
Free distributive lattice	Concept	Order, lattices, ordered algebraic structures
Zimmer program	Definition	Dynamical systems and ergodic theory
Gårding's inequality	Theorem	Partial differential equations
Modular curve	Concept	Number theory
Ambrose–Singer theorem	Theorem	Differential geometry
n-sphere	Object	Manifolds and cell complexes
Right adjoints preserve limits	Theorem	Category theory; homological algebra
Descartes' rule of signs	Theorem	Real functions
Gorenstein ring	Concept	Commutative algebra
Topological modular forms	Definition	Algebraic topology
Turing reduction	Definition	Mathematical logic and foundations
Steklov eigenvalue problem	Problem	Partial differential equations
Fractional calculus	Concept	Real functions
Lattice congruence	Concept	Order, lattices, ordered algebraic structures
E-infinity operad	Concept	Algebraic topology
Generator of a semigroup	Definition	Operator theory
Stable theory	Concept	Mathematical logic and foundations
Inner function	Definition	Functions of a complex variable
Cobordism	Concept	Manifolds and cell complexes
Multivariate division algorithm	Concept	Commutative algebra
Residuated mapping	Definition	Order, lattices, ordered algebraic structures
Bruhat decomposition	Theorem	Group theory and generalizations
Outer function	Definition	Functions of a complex variable
Pontryagin–Thom construction	Definition	Manifolds and cell complexes
Szpilrajn extension theorem	Theorem	Order, lattices, ordered algebraic structures
Pointed space	Concept	Algebraic topology
Degree of a projective variety	Definition	Algebraic geometry
Factorization system	Definition	Category theory; homological algebra
Integral quadratic form	Definition	Number theory
Hölder summation	Definition	Sequences, series, summability
Reaction–diffusion system	Concept	Partial differential equations
HNN extension	Definition	Group theory and generalizations
Error-correcting code	Concept	Information and communication theory, circuits
Abian–Brown theorem	Theorem	Order, lattices, ordered algebraic structures
Bicategory	Concept	Category theory; homological algebra
Tautological one-form	Definition	Differential geometry
Kawamata–Viehweg vanishing theorem	Theorem	Algebraic geometry
Ring of differential operators	Definition	Associative rings and algebras
Langevin equation	Definition	Probability theory and stochastic processes
Lévy–Prokhorov metric	Definition	Probability theory and stochastic processes
Direct limit	Definition	Category theory; homological algebra
Gerstenhaber algebra	Definition	Nonassociative rings and algebras
Faithful module	Concept	Associative rings and algebras
Picard–Vessiot extension	Concept	Field theory and polynomials
Sheaf	Concept	General topology
Saddle-node bifurcation	Definition	Ordinary differential equations
Space form	Definition	Differential geometry
Discriminant of a field extension	Definition	Number theory
Hamburger moment problem	Problem	Integral transforms, operational calculus
Triebel–Lizorkin space	Concept	Functional analysis
Krull's height theorem	Theorem	Commutative algebra
Crown	Example	Order, lattices, ordered algebraic structures
Universal Turing machine	Object	Mathematical logic and foundations
Foster's theorem on primal algebras	Theorem	General algebraic systems
Upper nilradical	Definition	Associative rings and algebras
Systolic geometry	Definition	Differential geometry
Cotangent space of a local ring	Definition	Commutative algebra
F-coalgebra	Definition	Category theory; homological algebra
Poisson kernel	Concept	Potential theory
Ehresmann connection	Concept	Differential geometry
Coupling	Definition	Probability theory and stochastic processes
Magnus expansion	Definition	Ordinary differential equations
Backward differentiation formula	Concept	Numerical analysis
Multiple integral	Definition	Real functions
Tietze transformations	Definition	Group theory and generalizations
Peixoto's theorem	Theorem	Dynamical systems and ergodic theory
Extremal length	Definition	Functions of a complex variable
Kaplansky density theorem	Theorem	Functional analysis
Invertible ideal	Definition	Commutative algebra
Functional completeness	Concept	General algebraic systems
Tarski monster group	Object	Group theory and generalizations
Direct method in the calculus of variations	Concept	Calculus of variations and optimal control; optimization
Hirzebruch signature theorem	Theorem	Manifolds and cell complexes
Hopf invariant	Concept	Algebraic topology
Lagrange polynomial	Definition	Approximations and expansions
Resolvent	Definition	Operator theory
Finite ring	Definition	Associative rings and algebras
Aleph number	Definition	Mathematical logic and foundations
Descriptive set theory	Concept	Mathematical logic and foundations
Exact category	Concept	Category theory; homological algebra
Capacity of a set	Definition	Potential theory
Banach algebra	Definition	Functional analysis
Geometric realization	Concept	Algebraic topology
ℓ-adic cohomology	Definition	Algebraic geometry
Chevalley's theorem on constructible sets	Theorem	Algebraic geometry
Join-prime element	Definition	Order, lattices, ordered algebraic structures
Down-closure	Definition	Order, lattices, ordered algebraic structures
Block design	Definition	Combinatorics
Residually small variety	Concept	General algebraic systems
Proof theory	Definition	Mathematical logic and foundations
Free category	Concept	Category theory; homological algebra
Spectral triple	Definition	Global analysis, analysis on manifolds
Paley–Wiener theorem	Theorem	Functions of a complex variable
Random graph	Definition	Combinatorics
Group scheme	Concept	Algebraic geometry
Normal form	Concept	Ordinary differential equations
The alternating group is the kernel of the sign	Example	Group theory and generalizations
Finitely presented group	Concept	Group theory and generalizations
Ore condition	Concept	Associative rings and algebras
Hahn series	Definition	Commutative algebra
Hyperreal number	Definition	Real functions
Filtered category	Definition	Category theory; homological algebra
Cluster algebra	Concept	Commutative algebra
Taft algebra	Example	Associative rings and algebras
Schur product theorem	Theorem	Linear and multilinear algebra; matrix theory
Free product	Concept	Group theory and generalizations
Borel density theorem	Theorem	Topological groups, Lie groups
Boundary value problem	Concept	Ordinary differential equations
Nevanlinna class	Definition	Functions of a complex variable
Scott continuity	Definition	Order, lattices, ordered algebraic structures
Eichler order	Definition	Number theory
Degree of a continuous map	Concept	Algebraic topology
Semilocally simply connected space	Definition	Manifolds and cell complexes
Semiprimitive ring	Definition	Associative rings and algebras
Primary ideal	Concept	Commutative algebra
Friendship theorem	Theorem	Combinatorics
Laplacian matrix	Concept	Combinatorics
Computably enumerable set	Concept	Mathematical logic and foundations
Formal group law in topology	Concept	Algebraic topology
Baby Monster group	Object	Group theory and generalizations
Random graph	Concept	Combinatorics
Fundamental theorem of space curves	Theorem	Differential geometry
Stable vector bundle	Definition	Algebraic geometry
Whitehead link	Example	Manifolds and cell complexes
Proper map	Definition	General topology
Fejér's theorem	Theorem	Harmonic analysis on Euclidean spaces
Axiom of dependent choice	Definition	Mathematical logic and foundations
Lang's conjectures	Conjecture	Algebraic geometry
Simplicial approximation theorem	Theorem	Algebraic topology
Reverse mathematics	Definition	Mathematical logic and foundations