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In mathematics, the '''Teichmüller–Tukey lemma''' (sometimes named just '''Tuk #For each <math>A\in \mathcal{F}</math>, every [[finite set|finite]] [[subset]] of <math>A</math ...

{{Short description|Theorem in functional analysis}} ...ics, '''Auerbach's lemma''', named after [[Herman Auerbach]], is a theorem in [[functional analysis]] which asserts that a certain property of [[Euclidea ...

...[[linear algebra]] used, for example, to show that any two [[Basis (linear algebra)|bases]] for a finite-[[Dimension (vector space)|dimensional]] [[vector spa ...ac Lane|year=1936|title=Some interpretations of abstract linear dependence in terms of projective geometry|journal=American Journal of Mathematics|volume ...

...zero. Historically, they are regarded as leading to the discovery of [[Lie algebra cohomology]].<ref>{{harvnb|Jacobson|1979|loc=p. 93}}</ref> ...ely, but there are similar statements pertaining to Lie algebra cohomology in arbitrary orders which are also attributed to Whitehead. ...

...as ''g''(''x'')''h''(''x'') with ''h''(''x'') also having [[coefficient]]s in&nbsp;''F''.<ref name="dorrie">{{citation|title=100 Great Problems of Elemen ...ional number]]s and has <math>\sqrt{2}</math> as a root; hence there is no linear or constant polynomial over the rationals having <math>\sqrt{2}</math> as a ...

...lemma in [[convex geometry]] and [[algebraic geometry]]. It can be stated in several ways. ...vectors in <math>M</math>, such that every element of <math>M</math> is a linear combination of these vectors with non-negative integer coefficients.<ref na ...

{{Short description|Condition for a linear operator to be open}} {{About|open mapping theorem in [[functional analysis]]|other results with the same name|Open mapping theor ...

...terative method]] for numerically solving the [[System of linear equations|linear system]] The intent of this article is to document the important steps in these derivations. ...

{{Short description|Gröbner bases for non-commutative algebra}} ...ts defining relations. However, in contrast to [[Buchberger's algorithm]], in the non-commutative case, this algorithm may not terminate.<ref name=":0">R ...

{{Short description|Theorem in abstract algebra}} ...newspaper=[[Time (magazine)|Time]] |access-date=December 14, 2009 }}</ref> In 2010, Ngô was awarded the [[Fields Medal]] for this proof. ...

{{short description|Abstract algebra concept}} In [[abstract algebra]], a '''decomposition of a module''' is a way to write a [[module (mathemat ...

...s any of several mathematical statements that ensure that several elements in a [[group (mathematics)|group]] [[group action|acting]] on a set freely [[G ...e group|rank]] two. The ping-pong lemma and its variations are widely used in [[geometric topology]] and [[geometric group theory]]. ...

In [[abstract algebra]], '''Kaplansky's theorem on projective modules''', first proven by [[Irvin ...heorem "is very likely the inspiration for a major portion of the results" in the theory of [[semiperfect ring]]s.<ref name="theorem" /> ...

...ion is from an '''exceptional collection''', a special sequence of objects in a triangulated category. For an [[algebraic variety]] ''X'', it has been fr ...eq n</math> and all objects <math>A_i\in\mathcal{A}_i</math> and <math>A_j\in\mathcal{A}_j</math>, every morphism from <math>A_j</math> to <math>A_i</mat ...

...is another family of equally many sets (blue outlines) such that each set in the second family is shattered by the first family]] ...and [[Alexey Chervonenkis]], after whom the VC dimension is named.{{r|vc}} In his paper containing the lemma, Shelah gives credit also to [[Micha Perles] ...

...hlet convolution]], or convolved [[divisor sum identities|divisors sums]], in terms of matrix products involving the [[transpose]] of the <math>n^{th}</m ...ath>j=1</math> and <math>i \neq 1</math>. The remaining one-valued entries in <math>A_n</math> then correspond to the divisibility condition reflected by ...

In the [[mathematics|mathematical]] area of [[geometric group theory]], a '''V ...up]] given by a [[group presentation]] represents the [[identity element]] in that group. ...

This is a glossary of properties and concepts in [[algebraic topology]] in mathematics. ...l categories]]. See the [[glossary of symplectic geometry]] for the topics in symplectic topology such as quantization. ...

...81|issn=2374-3468|doi-access=free|arxiv=1911.09488}}</ref> Some situations in which not all resources are available include: Some situations in which not all participants are available include: ...