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.
lemma | lemma (mathematics) | König's lemma | Zorn's lemma | the lemma that is not Burnside's | Schur's lemma | Lemma | Kurt Hensel | Johnson–Lindenstrauss lemma | Hotelling's lemma | Fundamental lemma of calculus of variations | Daniel Hensel | Bruce Hensel |
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.
The Munich Fanny Mendelssohn String Quartet, Renate Eggebrecht 1st violin, Mario Korunic 2nd violin, Stefan Berg viola, Friedemann Kupsa violoncello, was founded in 1989 in the occasion of the performance and publication of Fanny Mendelssohn-Hensel's String Quartet in E-flat major and Piano Quartet in A-flat major at the Gasteig/Munich.
Hotelling's lemma: an economic rule relating the supply of a good to the profit of the good's producer
A contemporary of Dr. Wilhelm Heinrich Schüßler (sometimes written Schussler), Hensel also proposed tritrated mineral substances to treat illness, but not diluted to the extent proposed by Hahnemann's homeopathy and made a large number of enemies in opposing many aspects of both established medical opinion of the day and some of the newer ideas - from vaccination to homeopathy.
König's lemma (also known as König's infinity lemma), named after Dénes Kőnig
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.
In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable.
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).
Synopsis Universae Philologiae, an early work on comparative linguistics by Gottfried Hensel (Godofredus Henselius, 1687–1767)
It is one route from the Texas A&M University campus to the university's Hensel Park, a recreation facility for faculty, staff, and students of the university.
Wilhelm Hensel was born on 6 July 1794 in the German town of Trebbin, in the present-day state of Brandenburg, to a Protestant preacher.
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.