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...rnal|last1=Krull|first1=Wolfgang|title=Zur Theorie der zweiseitigen Ideale in nichtkommutativen Bereichen|journal=Mathematische Zeitschrift|volume=28|iss ...iplicative system (''i.e.'' <math>M</math> is closed under multiplication) in a [[Ring (mathematics)|ring]] <math>R</math>, and suppose ...

...al topology]], a mathematical discipline, and more specifically in [[Morse theory]], a '''gradient-like vector field''' is a generalization of [[gradient vec The primary motivation is as a technical tool in the construction of [[Morse function]]s, to show that one can construct a f ...

In [[mathematics]], '''Heegner's lemma''' is a lemma used by [[Kurt Heegner]] in his paper on the [[class number problem]]. His lemma states that if ...'a''₄ not a square, then it has a solution if it has a solution in an [[field extension|extension]] of odd degree. ...

In mathematics, a '''Barnes integral''' or '''[[Hjalmar Mellin|Mellin]]&ndash; ...neralized hypergeometric function]]s _''p''''F''_''q'' in a similar way {{harv|Slater|1966}}. ...

...branch of mathematics, the '''condensation lemma''' is a result about sets in the ...sub>&alpha;</sub>, that is, <math>(X,\in)\prec (L_\alpha,\in)</math>, then in fact there is some ordinal <math>\beta\leq\alpha</math> such that <math>X=L ...

In the theory of [[formal language]]s, the '''interchange lemma''' states a necessary con ...er, <math>m/2<|x_i|\leq m</math>, and the words <math>w_ix_jy_i</math> are in <math>L</math> for every <math>i</math> and <math>j</math>. ...

...g and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. * [[Digital Morse theory]] ...

...spect to [[inclusion (set theory)|inclusion]]. Over [[Zermelo–Fraenkel set theory]], the Teichmüller–Tukey lemma is equivalent to the [[axiom of choice]], an #For each <math>A\in \mathcal{F}</math>, every [[finite set|finite]] [[subset]] of <math>A</math ...

In [[mathematics]], '''Cartan's lemma''' refers to a number of results named a * In [[exterior algebra]]:<ref>*{{cite book | last = Sternberg | first = S. | ye ...

[[File:TuckerLemExample.png|thumb|350px|In this example, where n=2, the red 1-simplex has vertices which are labelled In [[mathematics]], '''Tucker's lemma''' is a [[combinatorics|combinatorial]] ...

...nce of [[Philip Hall]] and [[Ernst Witt]]'s [[Commutator#Identities (group theory)|eponymous identity]]. In what follows, the following notation will be employed: ...

...the [[Stability theory|stability]] of delayed differential equations, and in particular, the stability of industrial processes with dead-time<ref>{{Cite <math display="block">\frac{d}{dt} v(t) \leq-\alpha v(t)+\beta\left[\sup _{s \in[t-\tau, t]} v(s)\right], t \geq t_{0} </math> ...

...lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the ...ty <math>d(U,V)</math>, is ''close'' ''to being'' a random bipartite graph in which every edge appears with probability <math>d(U,V)</math>, with some <m ...

{{short description|Field theory result}} ...rYuAUC&pg=PA120}}.</ref><ref>This theorem, for [[Minimal polynomial (field theory)|minimal polynomials]] rather than irreducible polynomials more generally, ...

...ommutative Algebra with a View Toward Algebraic Geometry'', Graduate Texts in Mathematics, 150, Springer-Verlag, 1995, {{ISBN|0-387-94268-8}}, Exercise 4 ...ely generated module]]".) The lemma was introduced by E. Artin and J. Tate in 1951<ref>E Artin, J.T Tate, "A note on finite ring extensions," J. Math. So ...

{{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 ...

...s]], the '''Lions–Magenes lemma''' (or '''theorem''') is the result in the theory of [[Sobolev space]]s of [[Banach space]]-valued functions, which provides ...0,T]</math> into <math>X</math>, and moreover the following equality holds in the sense of scalar [[distribution (mathematics)|distributions]] on <math>( ...

...sis of a [[function space]]. The result was originally proved by Stechkin in the case <math>q = 2</math>. ...math>N</math> largest terms of the sequence <math>(a_{i})_{i \in I}</math> in [[absolute value]]. Then ...

...mly close to some true trajectory (with slightly altered initial position)—in other words, a pseudo-trajectory is "shadowed" by a true one.<ref>{{cite jo ...ast1=Katok |first2=B. |last2=Hasselblatt |title=Introduction to the Modern Theory of Dynamical Systems |url=https://archive.org/details/introductiontomo0000k ...

The '''Mackey–Arens theorem''' is an important theorem in [[functional analysis]] that characterizes those [[locally convex]] [[Topol ...system|duality theory]]; a theory that is "the central part of the modern theory of topological vector spaces."{{sfn | Schaefer|Wolff| 1999 | p=122}} ...