In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent...
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Splitting, railway operation Heegaard splitting Splitting field Splitting principle Splitting theorem Splitting lemma for the numerical method to solve differential...
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In mathematics, especially in singularity theory, the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local...
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Exact sequence (section Weaving lemma)
{\displaystyle 0\to R/(I\cap J)\to R/I\oplus R/J\to R/(I+J)\to 0} The splitting lemma states that, for a short exact sequence 0 → A → f B → g C →...
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In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings...
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Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma Projective module Injective...
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T)=\dim(\operatorname {Domain} (T)).} This theorem can be refined via the splitting lemma to be a statement about an isomorphism of spaces, not just dimensions...
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Abhyankar's lemma Fundamental lemma (Langlands program) Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda lemma Matrix...
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and in W. A splitting is irreducible if it is not reducible. It follows from Haken's Lemma that in a reducible manifold every splitting is reducible...
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Ramsey's theorem Rao–Blackwell theorem Rice's theorem Rolle's theorem Splitting lemma squeeze theorem Sum rule in differentiation Sum rule in integration...
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equals b. This can be summarized by a commutative diagram as: The splitting lemma provides further equivalent characterizations of split exact sequences...
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Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category...
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automorphism of N) then N ⋊φ H is the direct product N × H. A version of the splitting lemma for groups states that a group G is isomorphic to a semidirect product...
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abelian groups), left splits and right splits are equivalent by the splitting lemma, and a right split is sufficient to produce a direct sum decomposition...
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Verlag. Barry, Mitchell (1965). Theory of categories. Academic Press. Splitting lemma Inverse function § Left and right inverses Transversal (combinatorics)...
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conjecture Quasi-fibration Splitting lemma Thom conjecture Thom isomorphism Thom space Thom transversality theorem Thom's first isotopy lemma Thom–Porteous formula...
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map (it suffices to lift each of the generators of M/tM into M). By splitting lemma (left split) M splits into: M = t M ⊕ F {\displaystyle M=tM\oplus F}...
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x)\\&=t\cdot \varphi (x),\end{aligned}}} so φ is in fact K[G]-linear. By the splitting lemma, K [ G ] = V ⊕ ker φ {\displaystyle K[G]=V\oplus \ker \varphi } ...
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various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem...
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extension L/K is assumed to be a Galois extension. Then the prime avoidance lemma can be used to show the Galois group G = Gal ( L / K ) {\displaystyle...
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Khatri–Rao product (redirect from Face-splitting product)
row-wise splitting of matrices with a given quantity of rows, was proposed by V. Slyusar in 1996. This matrix operation was named the "face-splitting product"...
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It is one of many closures in mathematics. Using Zorn's lemma or the weaker ultrafilter lemma, it can be shown that every field has an algebraic closure...
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the Borsuk–Ulam theorem from Tucker's lemma. The converse is also true: it is possible to prove Tucker's lemma from the Borsuk–Ulam theorem. Therefore...
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are, were, etc.), and contractions of those conjugations. These top 100 lemmas listed below account for 50% of all the words in the Oxford English Corpus...
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Consensus splitting, also called exact division,: 127 is a partition of a continuous resource ("cake") into some k pieces, such that each of n people...
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Gelfand pair (redirect from Gelfand lemma)
Now the Gelfand property for the pair (G,K) is an analog of the Schur's lemma. Using this approach, any concept of representation theory can be generalized...
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German mathematician. Arithmetic and geometric Frobenius Cauchy–Frobenius lemma Frobenioid Frobenius algebra Frobenius category Frobenius characteristic...
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2^{r}+2^{r}=2^{r+1}} nodes. Lemma 3: The maximum number of nodes of rank r is at most n 2 r . {\displaystyle {\frac {n}{2^{r}}}.} Proof From lemma 2, we know that...
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reputation, bounds on rational levels for the payoffs, but also tools like splitting lemma, signalling and approachability. While in many ways Mertens's work...
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Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...
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