In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent...

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...

Splitting, railway operation Heegaard splitting Splitting field Splitting principle Splitting theorem Splitting lemma for the numerical method to solve differential...

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...

In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings...

\nabla ^{-1}\circ \nabla } is thus clearly the identity. Thus by the splitting lemma, H 3 ≅ L 2 ⊕ im ⁡ ( curl ) {\displaystyle \mathbb {H} _{3}\cong L^{2}\oplus...

Abhyankar's lemma Fundamental lemma (Langlands program) Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda lemma Matrix...

Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma Projective module Injective...

equals b. This can be summarized by a commutative diagram as: The splitting lemma provides further equivalent characterizations of split exact sequences...

Ramsey's theorem Rao–Blackwell theorem Rice's theorem Rolle's theorem Splitting lemma squeeze theorem Sum rule in differentiation Sum rule in integration...

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...

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...

Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category...

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...

Verlag. Barry, Mitchell (1965). Theory of categories. Academic Press. Splitting lemma Inverse function § Left and right inverses Transversal (combinatorics)...

conjecture Quasi-fibration Splitting lemma Thom conjecture Thom isomorphism Thom space Thom transversality theorem Thom's first isotopy lemma Thom–Porteous formula...

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}...

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 } ...

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...

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...

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...

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"...

but it only contains one. Another way to explain this impossibility of splitting C 4 {\displaystyle C_{4}} (i.e. expressing it as a semidirect product)...

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...

reputation, bounds on rational levels for the payoffs, but also tools like splitting lemma, signalling and approachability. While in many ways Mertens's work...

from splitting of the homotopy operator for d {\displaystyle d} . This is a content of the Poincaré lemma on a complex manifold. The Poincaré lemma for...

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...

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...

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...

Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...