In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable.
lemma | Quillen–Suslin theorem | lemma (mathematics) | König's lemma | Zorn's lemma | the lemma that is not Burnside's | Schur's lemma | Lemma | Johnson–Lindenstrauss lemma | Jimmy Quillen | Hotelling's lemma | Fundamental lemma of calculus of variations |
The existence of Aronszajn trees (=-Aronszajn trees) was proven by Nachman Aronszajn, and implies that the analogue of König's lemma does not hold for uncountable trees.
Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's.
"By Now" is the title of a song written by Dean Dillon, Don Pfrimmer and Charles Quillen, and recorded by American country music artist Steve Wariner.
Masayoshi Nagata proved in the 1950s that for any commutative local ring A with maximal ideal m there always exists a smallest ring Ah containing A such that Ah is Henselian with respect to mAh.
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Completeness of a ring is not a necessary condition for the ring to have the Henselian property: Goro Azumaya in 1950 defined a commutative local ring satisfying the Henselian property for the maximal ideal m to be a Henselian ring.
Hotelling's lemma: an economic rule relating the supply of a good to the profit of the good's producer
König's lemma (also known as König's infinity lemma), named after Dénes Kőnig
He is well known for providing a simple proof of the Quillen–Suslin theorem, a result in commutative algebra, first conjectured by Jean-Pierre Serre in 1955, and then proved by Daniel Quillen and Andrei Suslin in 1976.
In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in Cn, the function –log d(z) is plurisubharmonic, where d is the distance to the boundary.
Leonid Vaseršteĭn later gave a simpler and much shorter proof of the theorem which can be found in Serge Lang's Algebra.
In 1934 Hollywood screen writer Lamar Trotti and producer George Marshall visited Quillen to use him as a prototype for a Will Rogers film, Life Begins at Forty, in which Rogers played a small-town newspaper editor.
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Quillen wrote for such major periodicals such as the Baltimore Sun, the Saturday Evening Post, and The American Magazine, and he "took the greatest pride" in one-liners picked up by Literary Digest.
In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, named after Stephen Schanuel, allows one to compare how far modules depart from being projective.
Henry Scheffé published a proof of the statement on convergence of probability densities in 1947.
The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book Theory of Cost and Production Functions (Princeton University Press, 1953).
Using the superconnection formalism of Quillen, they obtained a refinement of the Riemann–Roch formula, which links together the Thom classes in K-theory and cohomology, as an equality on the level of differential forms.
Zorn's lemma is a proposition used in many areas of theoretical mathematics.
# Banach's extension theorem which is used to prove one of the most fundamental results in functional analysis, the Hahn–Banach theorem
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It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.