The term split exact sequence is used in two different ways by different people. Some people mean a short exact sequence that right-splits (thus corresponding...

In mathematics, an exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian...

direct limit of projective modules, and a pure exact sequence is a direct limit of split exact sequences. Let R be a ring (associative, with 1), let M...

holds, the sequence is called a split exact sequence, and the sequence is said to split. In the above short exact sequence, where the sequence splits, it...

short exact sequence of modules of the form 0 → A → B → P → 0 {\displaystyle 0\rightarrow A\rightarrow B\rightarrow P\rightarrow 0} is a split exact sequence...

mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations...

properties of short exact sequences in an abelian category: E is closed under isomorphisms and contains the canonical ("split exact") sequences: M ′ → M ′ ⊕...

as the subgroup of constant loops. Consequently, we arrive at a split exact sequence 1 → Ω G → L G → G → 1 {\displaystyle 1\to \Omega G\to LG\to G\to...

words, there is a split exact sequence 1 → N → G → H → 1 {\displaystyle 1\to N\to G\to H\to 1} of groups (which is also known as a split extension of H {\displaystyle...

destroyer Split, decommissioned in 1980 Yugoslav frigate Split, Koni-class Split (graph theory) Split (mathematics), a property of an exact sequence Split Lie...

targets Krull–Schmidt theorem – Mathematical theorem Split exact sequence – Type of short exact sequence in mathematics Milnor, J.; Husemoller, D. (1973)...

The split gene theory is a theory of the origin of introns, long non-coding sequences in eukaryotic genes between the exons. The theory holds that the...

{\mathcal {A}},{\mathcal {B}}\rangle } as closer to a split exact sequence, because the exact sequence 0 → A → T → T / A → 0 {\displaystyle 0\to {\mathcal...

said that s splits the above exact sequence. Split extensions are very easy to classify, because an extension is split if and only if the group G is...

relations for split exact sequences, not general exact sequences. In the category of projective modules over a ring, every short exact sequence splits, and...

{\displaystyle S^{15}} are contractible to a point. Further the short exact sequences split and there are families of isomorphisms:: 111  π i ( S 4 ) ≅ π i...

categories if n ≥ 5 {\displaystyle n\geq 5} , one has the following split-exact sequences: In the category of topological spaces 0 → Z 2 ∞ → MCG ⁡ ( T n )...

words to the database sequences. Repeat step 3 to 4 for each k-letter word in the query sequence. Scan the database sequences for exact matches with the remaining...

various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and...

valuation of the discriminant, taken mod 2). One will then have a split exact sequence 0 → Z → W ( Q ) → Z / 2 ⊕ ⨁ p ≠ 2 W ( F p ) → 0   {\displaystyle...

_{1}^{R}(H_{i}(X;R),H_{j}(Y;R))\to 0.} Furthermore, these sequences split, but not canonically. The short exact sequences just described can easily be used to compute...

Ectrodactyly, split hand, or cleft hand (from Ancient Greek ἔκτρωμα (ektroma) 'miscarriage' and δάκτυλος (daktylos) 'finger') involves the deficiency...

every short exact sequence 0 → Z → B → A → 0 {\displaystyle 0\rightarrow \mathbb {Z} \rightarrow B\rightarrow A\rightarrow 0} must split if B is also...

extent to which taking invariants doesn't respect exact sequences. This is expressed by a long exact sequence. The collection of all G-modules is a category...

+ [ N ] {\displaystyle [M\oplus N]=[M]+[N]} , because of the split short exact sequence 0 → M → M ⊕ N → N → 0. {\displaystyle 0\to M\to M\oplus N\to N\to...

{\mathfrak {g}}^{\mathrm {red} }} . However, the corresponding short exact sequence 0 → n i l ( g ) → g → g r e d → 0 {\displaystyle 0\to {\mathfrak {nil}}({\mathfrak...

conversely a gene may be split across chromosomes but those transcripts are concatenated back together into a functional sequence by trans-splicing. It is...

other indicator lights to show the sequence of voltages at the terminals for the given direction of shaft rotation. Split-phase electric power Used when three-phase...

a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V1, V2, ..., Vn taking...

confusion in determining the exact age of the Pan–Homo split is evidence of a more complex speciation process than a clean split between the two lineages...