In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or...

Farkas' lemma Fatou's lemma Gauss's lemma (any of several named after Carl Friedrich Gauss) Greendlinger's lemma Itô's lemma Jordan's lemma Lovász local...

Jordan curve theorem holds for every Jordan polygon (Lemma 1), and every Jordan curve can be approximated arbitrarily well by a Jordan polygon (Lemma...

Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...

reduction or Gaussian method Gauss–Jordan elimination Gauss–Seidel method Gauss's cyclotomic formula Gauss's lemma in relation to polynomials Gaussian...

theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however...

{\displaystyle y} have the same length, then the lattice is said to satisfy the Jordan–Dedekind chain condition. A lattice ( L , ≤ ) {\displaystyle (L,\leq )}...

Canada Aïda Neither Aïda non plus Elisa Gilmour France Alazar Beza Hailu Lemma Ethiopia, France, Canada Amarela André Hayato Saito Brazil Anotc ota ickwaparin...

Schur complement is named after Issai Schur who used it to prove Schur's lemma, although it had been used previously. Emilie Virginia Haynsworth was the...

case of primitive matrices; we just need to mention the following simple lemma, which clarifies the properties of primitive matrices. Given a non-negative...

group Hn-1(∂M) by de Rham's theorem. The BFPT can be proved using Sperner's lemma. We now give an outline of the proof for the special case in which f is...

ISBN 978-0-521-82356-2, MR 2131318; see especially Lemma 8.2 (Ring Lemma), pp. 73–74, and Appendix B, The Ring Lemma, pp. 318–321. Knuth, Donald E (1997), The...

theorem, every finite group is the automorphism group of a graph Yoneda lemma, a generalization of Cayley's theorem in category theory Representation...

hypotheses List of inequalities Lists of integrals List of laws List of lemmas List of limits List of logarithmic identities List of mathematical functions...

some key arithmetic concepts, such as Fermat's little theorem and Gauss's lemma. The main objective of introducing this ring was to formulate the law of...

of Jordan domains. In studying boundary correspondence he originated the theory of prime ends. He exhibited an elementary proof of the Schwarz lemma. Carathéodory...

}f^{(n)}(x)=0,n=0,1,2,\dots } . (See Schwartz function). By the Riemann–Lebesgue lemma, the transformed function f ^ {\displaystyle {\widehat {f}}} also decays...

by it to define analytic sets as continuous images of Borel sets. Dehn's lemma. Dehn published an attempted proof in 1910, but Kneser found a gap in 1929...

j-invariant Line complex Grünbaum–Rigby configuration Homomorphism Ping-pong lemma Prime form W-curve Uniformization theorem Felix Klein Protocols List of...

Wind from the East (Dziga Vertov Group, Italy/France/West Germany) Zorns Lemma (Hollis Frampton, USA) Opening Night: The Beginning (Gleb Panfilov, USSR)...

the Jordan curve theorem in 1905; while this was long considered the first rigorous proof of the theorem, many now also consider Camille Jordan's original...

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idempotent is an idempotent a for which aR is a simple module. By Schur's lemma, EndR(aR) = aRa is a division ring, and hence is a local ring, so right...

this lemma, see Roman 2008, Theorem 8.2 on p. 186; Shilov 1977, p. 109; Hefferon 2001, p. 364; Beezer 2006, Theorem EDELI on p. 469; and Lemma for linear...

original contributions to group theory, and Burnside's Lemma is sometimes jokingly referred to as "the lemma that is not Burnside's". Buridan's ass originates...

Schur decomposition and for his work on group representations (Schur's lemma). Schur published under the name of both I. Schur, and J. Schur, the latter...

to ϕ {\displaystyle \phi } . This is an easy consequence of the Schwarz lemma. As a corollary of the theorem, any two simply connected open subsets of...

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isoperimetric inequality Gibbs's inequality Hoeffding's inequality Hoeffding's lemma Jensen's inequality Khintchine inequality Kolmogorov's inequality Kunita–Watanabe...

and the theory of Sturmian words. Noether normalization lemma The Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether...