List_of_lemmas
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.
This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources.
Main category: Lemmas in algebra
- Abhyankar's lemma
- Aubin–Lions lemma
- Bergman's diamond lemma
- Fitting lemma
- Injective test lemma
- Hua's lemma (exponential sums)
- Krull's separation lemma
- Schanuel's lemma (projective modules)
- Schwartz–Zippel lemma
- Shapiro's lemma
- Stewart–Walker lemma (tensors)
- Whitehead's lemma (Lie algebras)
- Zariski's lemma
Algebraic geometry
Category theory
Linear algebra
Group theory
- Burnside's lemma also known as the Cauchy–Frobenius lemma
- Frattini's lemma (finite groups)
- Goursat's lemma
- Mautner's lemma (representation theory)
- Ping-pong lemma (geometric group theory)
- Schreier's subgroup lemma
- Schur's lemma (representation theory)
- Zassenhaus lemma
Polynomials
Ring theory and commutative algebra
Universal algebra
Main category: Lemmas in analysis
- Fekete's lemma
- Fundamental lemma of calculus of variations
- Hopf lemma
- Sard's lemma (singularity theory)
- Stechkin's lemma (functional and numerical analysis)
- Vitali covering lemma (real analysis)
- Watson's lemma
Complex analysis
Fourier analysis
Differential equations
Differential forms
Functional analysis
Mathematical series
Numerical analysis
- Danielson–Lanczos lemma (Fourier transforms)
- Farkas's lemma (linear programming)
- Feld–Tai lemma (electromagnetism)
- Little's lemma (queuing theory)
- Finsler's lemma
Control theory
Computational complexity theory
Cryptography
Formal languages
- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
- Cousin's lemma (integrals)
- Dickson's lemma
- Littlewood–Offord lemma
- Pólya–Burnside lemma
- Sperner's lemma
- Ky Fan lemma (combinatorial geometry)
Graph theory
Main category: Lemmas in graph theory
Order theory
Euclidean geometry
Hyperbolic geometry
Metric spaces
Riemannian geometry
- Craig interpolation lemma
- Diagonal lemma
- Lindenbaum's lemma
- Mostowski collapse lemma
- Teichmüller–Tukey lemma also known as Tukey's lemma
- Zorn's lemma; equivalent to the axiom of choice
Set theory
Main category: Lemmas in set theory
Main category: Lemmas in number theory
- Bézout's lemma
- Dwork's lemma
- Euclid's lemma
- Gauss's lemma
- Hensel's lemma
- Zolotarev's lemma
- Siegel's lemma (Diophantine approximation)
Analytic number theory
Diophantine equations
Sieve theory
- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma