In mathematics, a split exact sequence is a short exact sequence in which the middle term is built out of the two outer terms in the simplest possible...

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

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...

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...

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

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

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...

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

targets Krull–Schmidt theorem – Mathematical theorem Split exact sequence – short exact sequence where the middle term is the direct sum of the outer...

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

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...

{\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...

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...

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...

{\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...

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

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

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 )...

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

_{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...

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

The human genome is a complete set of nucleic acid sequences for humans, encoded as the DNA within each of the 24 distinct chromosomes in the cell nucleus...

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...

maximum packet size for that endpoint, called a "short" packet. When the exact amount of data specified by the wLength field of the setup packet has been...

Such stars are said to be on the main sequence and are called dwarf stars. Starting at zero-age main sequence, the proportion of helium in a star's core...

a computer program. Modern programming languages commonly use a quoted sequence of characters, formally "bracketed delimiters", as in x = "foo", where...

there are two basic exact sequences for Ext. First, a short exact sequence 0 → K → L → M → 0 of R-modules induces a long exact sequence of the form 0 → H...

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...