Search results

This following is a '''list of [[lemma (mathematics)|lemmas]]''' (or, "'''lemmata'''", i.e. minor [[theorem]]s, or sometimes intermedia == Algebra == ...

{{For|Lebesgue's lemma for open covers of compact spaces in topology|Lebesgue's number lemma}} ...or, controlling the error of approximation by a linear subspace based on a linear projection relative to the optimal error together with the [[operator norm] ...

'''Whitehead's lemma''' is a technical result in [[abstract algebra]] used in [[algebraic K-theory]]. It states that a [[matrix (mathematics)|matrix]] o ...url=https://archive.org/details/explicitbrauerin0000snai/page/164 }}</ref> In symbols, ...

...er the mathematician [[Hans Fitting]] – is a basic statement in [[abstract algebra]]. Suppose ''M'' is a [[module (mathematics)|module]] over some [[ring (mat ...atics)|group]] ''G'' can be viewed as a module over the [[group ring|group algebra]] ''KG''. ...

|fields = [[Numerical Analysis]] <br> [[Linear Algebra]]<ref>{{cite web | url=https://sites.google.com/a/lbl.gov/hh11/householdera |thesis_title = The Dependence of a Focal Point Upon Curvature in the Calculus of Variations ...

...r2-link=Samuel Eilenberg|year=1948}} to coefficients in an arbitrary [[Lie algebra representation|Lie module]].<ref>{{Cite journal|last=Koszul|first=Jean-Loui ...ferential forms can be identified with the [[exterior algebra]] of the Lie algebra, with a suitable differential. ...

{{Distinguish|text=the [[splitting lemma (functions)|splitting lemma]] in [[singularity theory]]}} ...ifically in [[homological algebra]], the '''splitting lemma''' states that in any [[abelian category]], the following statements are [[logical equivalenc ...

...] of [[group (mathematics)|groups]] and [[algebra over a field|algebras]]. In the group case it says that if ''M'' and ''N'' are two finite-dimensional [ ...groups]]. Schur's lemma admits generalisations to [[Lie group]]s and [[Lie algebra]]s, the most common of which are due to [[Jacques Dixmier]] and [[Daniel Qu ...

{{short description|Solvability theorem for finite systems of linear inequalities}} ...a solvability theorem for a finite [[System of inequalities|system]] of [[linear inequalities]]. It was originally proven by the Hungarian mathematician [[G ...

{{short description|Ideals in a Boolean algebra can be extended to prime ideals}} ...[[Ideal (order theory)|ideals]] in a [[Boolean algebra (structure)|Boolean algebra]] can be extended to [[Ideal (order theory)#Prime ideals | prime ideal]]s. ...

{{Short description|Theorem in homological algebra}} ...s a crucial tool in homological algebra and its applications, for instance in [[algebraic topology]]. Homomorphisms constructed with its help are general ...

...hogonal group''', {{nowrap|O(''p'', ''q'')}} is the [[Lie group]] of all [[linear transformation]]s of an ''n''-[[dimension (vector space)|dimensional]] [[re ...(''p'', ''q'')}} consisting of all elements with [[determinant]] 1. Unlike in the definite case, {{nowrap|SO(''p'', ''q'')}} is not [[connected space|con ...

{{About|a construction in mathematics|the article about company products or services directly related ...product is similar to the [[direct product of groups|direct product]], but in the central product two [[isomorphism|isomorphic]] [[center (group theory)| ...

In [[mathematics]], an '''involution''', '''involutory function''', or '''self for all {{mvar|x}} in the [[domain of a function|domain]] of {{math|''f''}}.<ref>{{citation|last= ...

{{Short description|Result of commutative algebra}} ...bra]] <math>A</math>, there exist elements <math>y_1,y_2,\ldots,y_d</math> in <math>A</math> that are [[algebraically independent]] over <math>k</math> a ...

In [[mathematics]], more specifically in [[group theory]], a [[Group (mathematics)|group]] is said to be '''perfect' ...t. However, a perfect group need not be simple; for example, the [[special linear group]] over the [[field (mathematics)|field]] with 5 elements, SL(2,5) (or ...

...formula''' or just '''Woodbury formula'''. However, the identity appeared in several papers before the Woodbury report.<ref name="guttman">{{cite journa ...ily used on matrices, it holds in a general [[ring (mathematics)|ring]] or in an [[Ab-category]]. ...

{{Short description|Theorem in algebra mathematics}} ...because it allows local data on [[algebraic variety|algebraic varieties]], in the form of modules over [[local ring]]s, to be studied pointwise as vector ...

...ematical articles. This article brings together the same content organized in a manner better suited for browsing. ...and ''[[Zentralblatt MATH]]''. This list has some items that would not fit in such a classification, such as [[list of exponential topics]] and [[list of ...

...>, the '''Lindemann–Weierstrass theorem''' is a result that is very useful in establishing the [[transcendental number|transcendence]] of numbers. It sta In other words, the [[extension field]] <math>\mathbb{Q}(e^{\alpha_1}, \dots, ...