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Type of short exact sequence in mathematics
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
Split_exact_sequence
Sequence of homomorphisms such that each kernel equals the preceding image
In mathematics, an exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian
Exact_sequence
About direct sums and exact sequences
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
Splitting_lemma
Direct summand of a free module (mathematics)
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
Projective_module
Module components with flexibility in module theory
direct limit of projective modules, and a pure exact sequence is a direct limit of split exact sequences. Let R {\displaystyle R} be a ring (associative
Pure_submodule
properties of short exact sequences in an abelian category: E is closed under isomorphisms and contains the canonical ("split exact") sequences: M ′ → M ′ ⊕
Exact_category
Operation in group theory
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
Semidirect_product
Functor that preserves short exact sequences
mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations
Exact_functor
Subject area in mathematics
relations for split exact sequences, not general exact sequences. In the category of projective modules over a ring, every short exact sequence splits, and
Algebraic_K-theory
Topics referred to by the same term
destroyer Split, decommissioned in 1980 Yugoslav frigate Split, Koni-class Split (graph theory) Split (mathematics), a property of an exact sequence Split Lie
Split
Operation in abstract algebra
targets Krull–Schmidt theorem – Mathematical theorem Split exact sequence – Type of short exact sequence in mathematics Wedderburn, J. H. M. (1934). Lectures
Direct_sum_of_modules
The split gene theory offers an explanation for the origin of eukaryotic introns. It suggests that random primordial DNA sequences would only permit short
Split_gene_theory
Group for which a given group is a normal subgroup
extension of Q {\displaystyle Q} by N {\displaystyle N} if there is a short exact sequence 1 → N → ι G → π Q → 1. {\displaystyle 1\to N\;{\overset {\iota }{\to
Group_extension
Tensoring the Euler sequence of P 1 {\displaystyle \mathbb {P} ^{1}} by O ( 1 ) {\displaystyle {\mathcal {O}}(1)} gives a non-split exact sequence 0 → O ( − 1
Stable_vector_bundle
{\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
Semiorthogonal_decomposition
Algebra term
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
Witt_group
Concept in algebraic topology
{\displaystyle S^{15}} are contractible to a point. Further the short exact sequences split and there are families of isomorphisms: π i ( S 4 ) ≅ π i ( S 7
Fibration
Mathematical group of loops in a Lie group
inclusion of constant loops gives a splitting of ev1, so there is a split exact sequence 1 → Ω G → L G → ev 1 G → 1 , {\displaystyle 1\to \Omega G\to LG\xrightarrow
Loop_group
Bioinformatics search algorithm
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
BLAST_(biotechnology)
Group of isotopy classes of a topological automorphism group
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 )
Mapping_class_group
Relates the homology of two objects to the homology of their product
_{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
Künneth_theorem
Homological construction in category theory
various quite different settings that a short exact sequence often gives rise to a "long exact sequence". Derived functors clarify and generalize many
Derived_functor
Malformation of the central digit(s) of the hand or foot
Ectrodactyly, split hand, or cleft hand (from Ancient Greek ἔκτρωμα (éktroma) 'miscarriage' and δάκτυλος (dáktulos) 'finger') involves the deficiency
Ectrodactyly
Substrings of length k contained in a biological sequence
k} contained within a biological sequence. Primarily used within the context of computational genomics and sequence analysis, in which k-mers are composed
K-mer
Abelian group extending a commutative monoid
+ [ 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
Grothendieck_group
Sequence of DNA that determines traits in an organism
conversely a gene may be split across chromosomes but those transcripts are concatenated back together into a functional sequence by trans-splicing. It is
Gene
Frame sequence for color composite video signals
editing and broadcast was known as color framing. The exact nature of the color frame sequence depends on the video standard being used. In the case of
Color_frame_sequence
Question in abstract algebra
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
Whitehead_problem
{\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
Nilradical_of_a_Lie_algebra
Trick-taking card game
normally return the suit led. 1st hand: It is usual to lead the king from a sequence of honours that includes it, including AK (the lead of an ace therefore
Whist
Problem optimization method
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
Dynamic_programming
Complete set of nucleic acid sequences for humans
The human genome is a complete set of DNA sequences for each of the 22 autosomes and the two distinct sex chromosomes (X and Y). A small DNA molecule
Human_genome
Star at the centre of the Solar System
initiated nuclear fusion in its core. It is now classified as a G-type main-sequence star (G2V). Every second, the Sun's core fuses about 600 billion kilograms
Sun
Tools for studying groups based on techniques from algebraic topology
extent to which taking invariants doesn't respect exact sequences. This is expressed by a long exact sequence. The collection of all G {\displaystyle G} -modules
Group_cohomology
Discrete Fourier transform algorithm
computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts a signal from its original domain (often
Fast_Fourier_transform
Group of mathematical theorems
which complete the short exact sequence running from the lower left to the upper right of the diagram. The use of the exact sequence convention saves us from
Isomorphism_theorems
Theorem in category theory
sent to a split coequalizer sequence in D is itself a coequalizer sequence in C. In different words, U creates (preserves and reflects) U-split coequalizer
Beck's_monadicity_theorem
Instructions directly executable by a computer
its programmable interface. A computer program consists primarily of sequences of machine-code instructions. Machine code is classified as native with
Machine_code
Durable and flexible material created by tanning animal skins
A further subprocess, finishing, can be added into the leather process sequence, but not all leathers receive finishing. The preparatory stages are when
Leather
Sequence of operations for a task
mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class
Algorithm
Casino game of chance
variety of betting options. "Inside" bets involve selecting either the exact number on which the ball will land, or a small group of numbers adjacent
Roulette
Form of alternating current
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
Three-phase_electric_power
Large self-illuminated object in space
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
Star
Most common system for writing numbers
from zero to nine, and allows representing any natural number by a unique sequence of these glyphs. The symbols (glyphs) used to represent the system are
Hindu–Arabic_numeral_system
Superorder of mammals
DNA sequence analyses and retrotransposon presence/absence data. The superorder originated on the northern supercontinent of Laurasia, after it split from
Laurasiatheria
Superorder of mammals
treeshrews, primates, and colugos. The Euarchontoglires clade is based on DNA sequence analyses and retrotransposon markers that combine the clades Glires (Rodentia
Euarchontoglires
On polynomial rings over fields
i . {\displaystyle G_{i}\mapsto g_{i}.} In other words, one has an exact sequence 0 → R 1 → L 0 → M → 0. {\displaystyle 0\to R_{1}\to L_{0}\to M\to 0
Hilbert's_syzygy_theorem
Simple knot used to form a fixed loop at the end of a rope
with variances depending upon the nature of the rope, as in practice the exact strength depends on a variety of factors. In the United Kingdom, the knot
Bowline
list of sequence alignment software is a compilation of software tools and web portals used in pairwise sequence alignment and multiple sequence alignment
List of sequence alignment software
List_of_sequence_alignment_software
Construction in group theory
_{n}&\to &\mathrm {SL} &\to &\mathrm {PSL} \end{matrix}}} via the long exact sequence of a fibration. For both the reals and complexes, SL is a covering space
Projective_linear_group
metric for the amount of difference between two sequences Trigram search: search for text when the exact syntax or spelling of the target object is not
List_of_algorithms
Paraphyletic group of mammals
larynx is attached to the hyoid bone that is hanging from a sequence of bones. This sequence of bones the hyoid hangs from are tympanohyal, stylohyal, epihyal
Big_cat
South Korean professional esports player (born 1996)
Yoo "Ryu" Sang-wook from the Bullets, but he executed a perfectly timed sequence of moves to reverse the situation and kill Ryu. The play is regarded as
Faker_(gamer)
Type of machine learning model
development of word embeddings (e.g., Word2Vec by Mikolov in 2013) and sequence-to-sequence (seq2seq) models using LSTM. In 2016, Google transitioned its translation
Large_language_model
Communication aspects of Universal Serial Bus
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
USB_communications
Concept in mathematics
section with trivial normal bundle (a section corresponds to a short exact sequence 0 → J → A + I → K → 0 where J, K are ideal classes and the normal bundle
Reductive_group
Number expressed in the base-2 numeral system
In this method, multiplying one number by a second is performed by a sequence of steps in which a value (initially the first of the two numbers) is either
Binary_number
Viral pulmonary disease of humans
one-species-one-hantavirus relationship is not true for all hantaviruses. The exact evolutionary history of hantaviruses is likely obscured by many instances
Hantavirus_pulmonary_syndrome
its fossil incompleteness and the proximity to the human-chimpanzee split, the exact position of Ardipithecus in the fossil record is unclear. However,
Chimpanzee–human last common ancestor
Chimpanzee–human_last_common_ancestor
Havana, Cuba A major event that precipitated the Spanish–American War. Exact cause remains unknown. 273 1875 Pacific (1850) Accident – shipwreck Off
List of disasters in the United States by death toll
List_of_disasters_in_the_United_States_by_death_toll
Stimulating neuropeptide
residues in 6 and 12 and 7 and 14 positions.[citation needed] The amino acid sequence is: Pyroglu-Pro-Leu-Pro-Asp-Cys-Cys-Arg-Gln-Lys-Thr-Cys-Ser-Cys-Arg-Le
Orexin-A
Mathematical group
image is the inner automorphism group). This can be summarized by the exact sequence Z ( G ) ↪ G ⟶ σ A u t ( G ) ↠ O u t ( G ) {\displaystyle Z(G)\hookrightarrow
Outer_automorphism_group
British crime TV series (1962–1969)
switch to colour, this was replaced by simple narration. The pre-credit sequence usually ended with someone referring to (and/or addressing) the Saint by
The_Saint_(TV_series)
Clade of birds
earliest split in Neoaves. A reanalysis with an extended dataset by Reddy and colleagues in 2017 suggested this was due to the type of sequence data, with
Neoaves
Natural disaster in the US
they knew severe storms were in the area, although they did not know the exact location, extent, and movement of the storms. Fujita, T. T.; Bradbury, D
1965 Palm Sunday tornado outbreak
1965_Palm_Sunday_tornado_outbreak
Spanish heist crime drama television series
audience feel that the characters are safe from the police although their exact location is undisclosed at first. Underwater scenes inside the vault were
Money_Heist
2010 film by Edgar Wright
The opening title sequence was designed by Richard Kenworthy of Shynola, and was inspired by drawn-on-film animation. The sequence also begins with an
Scott_Pilgrim_vs._the_World
American film production and distribution company
retained by Disney via 20th Century Animation. Although Disney did not give an exact date as to when the studio would be closing down initially, former animator
20th_Century_Studios
Animated sitcom
"GUMBALL IS GETTING CLOSER! 6th OCTOBER TO BE EXACT. Cartoon Network Releases New Opening Title Sequence and International Premiere Date for The Wonderfully
The Wonderfully Weird World of Gumball
The_Wonderfully_Weird_World_of_Gumball
Construction in homological algebra
a short exact sequence 0 → K → L → M → 0 {\displaystyle 0\rightarrow K\rightarrow L\rightarrow M\rightarrow 0} induces a long exact sequence of the form
Ext_functor
River. For security reasons, the organizers of the talks did not name the exact location.] "Newly published documents from invasion's first weeks reveal
Peace negotiations in the Russo-Ukrainian war (2022–present)
Peace_negotiations_in_the_Russo-Ukrainian_war_(2022–present)
2005 Indian film by Shankar
festival and the extensive use of time slice photography in an action sequence. Cinematographer V. Manikandan discontinued the project halfway through
Anniyan
Type of defect in crystalline materials
materials form repeating patterns of layers of atoms. Errors can occur in the sequence of these layers and are known as stacking faults. Stacking faults are in
Stacking_fault
Theoretical paradox resulting from time travel
According to this hypothesis, even though general relativity permits some exact solutions that allow for time travel that contain closed timelike curves
Temporal_paradox
South Korean character set
known as Johab. This represents a Hangul syllable as the sequence of three five-bit values, split across two 8-bit bytes, most significant bit first. The
KS_X_1001
Musical tuning system with constant ratios between notes
its ratio, this scale in even steps is a geometric sequence of multiplications. (An arithmetic sequence of intervals would not sound evenly spaced and would
Equal_temperament
Electric motor driven by an AC electrical input
seconds. These motors are relatively costly, and are used where exact speed (assuming an exact-frequency AC source) and rotation with low flutter (high-frequency
AC_motor
American television programming block
Broadcasting is in contact with local and federal law enforcement on the exact locations of the billboards. We regret that they were mistakenly thought
Adult_Swim
DNA that does not code for proteins
since that lineage split from those of other plants. About 59% of the bladderwort genome consists of transposon-related sequences but since the genome
Non-coding_DNA
2026 American superhero series by Oren Uziel
September 12, 2020. Travis, Ben (March 9, 2026). "Spider-Noir Won't Be The Exact Version From Spider-Verse: 'Same Character, Different Universe'". Empire
Spider-Noir
2022 video game
Interactive, Jetpack Interactive, Super Genius, and Original Force. The exact contribution from each studio was not detailed, except SuperAlloy, which
God_of_War_Ragnarök
Government system where political power lies with the people
authority over setting taxation, foreign affairs and legislating, though the exact nature of its role remains disputed. The Republic of Ragusa, established
Democracy
Heterogeneous class of stars with unusual spectra
and WC respectively. The two classes WN and WC were further split into temperature sequences WN5–WN8 and WC6–WC8 based on the relative strengths of the
Wolf–Rayet_star
Gene editing method
a DNA repair template allows for the insertion of a specific DNA sequence at an exact location within the genome. The repair template should extend 40
CRISPR_gene_editing
American actress and singer (born 1986)
a second we thought Dianna Agron and Michelle Pfeiffer were wearing the exact same dress. Our eyes went straight to the wide necklines and we barely noticed
Dianna_Agron
the original sequence is exact. ◻ {\displaystyle \square } Bhargav Bhatt and Peter Scholze (2019, §8) show that the Amitsur complex is exact if R {\displaystyle
Amitsur_complex
imagery, cockpit voice recordings, and official reports to reconstruct the sequences of events. As of 2 June 2026,[update] 297 episodes of Mayday have aired
List_of_Mayday_episodes
Software that translates code from one programming language to another
languages include: Alphabet, any finite set of symbols; String, a finite sequence of symbols; Language, any set of strings on an alphabet. The sentences
Compiler
a(P) is constructed as follows. For any extension K of k there is an exact sequence 0 → H 3 ( K , Q / Z ( 2 ) ) → H e t 3 ( P K , Q / Z ( 2 ) ) → Q / Z
Rost_invariant
Algorithm in numerical analysis
significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers, compared to the naive approach
Kahan_summation_algorithm
British television series (1971–1972)
advertisement for the 306 car, with the theme of the opening title sequence, the split-screen process and even the voice of Michel Roux, who dubbed Tony
The_Persuaders!
Fictional time traveler
Omaha, Nebraska would be the new U.S. capital. Titor did not detail the exact causes of this World War III scenario, but in one post said that the hostilities
John_Titor
Reyes is the son of the fallen Brazilian kingpin Hernan Reyes who wants to exact revenge against Dom and his family for his father's death, the theft of
List of Fast & Furious characters
List_of_Fast_&_Furious_characters
Theory of developmental psychology
Maslow's hierarchy may be limited as a theory for developmental sequence since the sequence of the love need and the self-esteem need should be reversed
Maslow's_hierarchy_of_needs
Completing Minecraft as fast as possible
measure the angles Eyes of Ender travel while thrown and calculate the exact coordinates of the Stronghold structure. Players then typically travel through
Minecraft_speedrunning
1969 car accident and drowning in Massachusetts
Newberg for her room key either, according to Judge Boyle's report. The exact time the crash occurred is unknown, due to a conflict between the testimony
Chappaquiddick_incident
American television series (2004–2010)
primary storyline set on the island, augmented by flashback or flashforward sequences which provide additional insight into the involved characters. Lindelof
Lost_(TV_series)
How spheres of various dimensions can wrap around each other
π3(S7) and π7(S15) are zero. Thus the long exact sequences again break into families of split short exact sequences, implying two families of relations. π
Homotopy_groups_of_spheres
System for identifying vehicles
section or fourth to eighth segment of the VIN. In order to identify the exact year in passenger cars and multipurpose passenger vehicles with a GVWR of
Vehicle_identification_number
Stellar classification
black holes or neutron stars. Most of these stars are young massive main sequence, giant, or supergiant stars, but also some central stars of planetary nebulae
O-type_star
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
Boy/Male
Hindu
Inside viewer, Spilt second
Boy/Male
Muslim/Islamic
Split Cleavage
Boy/Male
English
From the split meadow.
Boy/Male
American, Australian, Chinese, Hebrew, Jewish
Exalt; Praised; Son of Jacob and Leah
Boy/Male
American, British, English
From the Split Meadow
Boy/Male
Muslim
Strong, Solid, Firm, Sharp
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
Indian, Punjabi, Sikh
Exact Love
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Momentary; Lord Rama's Ancestor; Spilt-second; Lord Vishnu
Boy/Male
Arabic, Muslim, Sindhi
Split
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
Hindu, Indian
Exact; Alert
Boy/Male
Muslim
Split, Cleavage
Boy/Male
Gujarati, Hindu, Indian
One who Lives Life Long; Gains Victory Within Splits
Girl/Female
Hindu, Indian, Telugu
Motherly Love; Energetic Sprit
Boy/Male
Hindu
Inside viewer, Spilt second
Boy/Male
Arabic, Muslim
Strong; Solid; Firm; Sharp
Girl/Female
Hindu, Indian
Momentary; Split Second
Girl/Female
American, Christian, Hebrew, Indian
Narrow Split of Land
Boy/Male
Hebrew
May Jehovah exalt. God prepares.
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
Girl/Female
Native American
Grandmother.
Surname or Lastname
English, Scottish, and Irish
English, Scottish, and Irish : variant of Murray.
Girl/Female
Australian, Romanian
Flower
Boy/Male
Australian, Gaelic, Scottish
Child; Virile
Boy/Male
English German
Famous ruler.
Male
English
Variant spelling of English Michah, MICHA means "who is like God?"
Male
Italian
Italian form of German Conrad, CORRADO means "bold counsel."
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Tamil
Courageous; Patient
Girl/Female
Indian
A River; River in Jammu and Kashmir
Boy/Male
Indian
Wealthy
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
v. i.
To part asunder; to be rent; to burst; as, vessels split by the freezing of water in them.
v. t.
One of the small plates of metal used in making splint armor. See Splint armor, below.
imp. & p. p.
of Spit
imp. & p. p.
of Slit
v. i.
To attend to a spit; to use a spit.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
imp. & p. p.
of Split
v. t.
To divide or separate into components; -- often used with up; as, to split up sugar into alcohol and carbonic acid.
v. t.
To render pure or refined; to intensify or concentrate; as, to exalt the juices of bodies.
v. t.
To split into splints, or thin, slender pieces; to splinter; to shiver.
a.
Precisely agreeing with a standard, a fact, or the truth; perfectly conforming; neither exceeding nor falling short in any respect; true; correct; precise; as, the clock keeps exact time; he paid the exact debt; an exact copy of a letter; exact accounts.
v. t.
A piece split off; a splinter.
v. t.
To divide lengthwise; to separate from end to end, esp. by force; to divide in the direction of the grain layers; to rive; to cleave; as, to split a piece of timber or a board; to split a gem; to split a sheepskin.
n.
To cut lengthwise; to cut into long pieces or strips; as, to slit iron bars into nail rods; to slit leather into straps.
v. t.
A splint bone.
n.
the substitution of more than one share of a corporation's stock for one share. The market price of the stock usually drops in proportion to the increase in outstanding shares of stock. The split may be in any ratio, as a two-for-one split; a three-for-two split.
v. t.
A disease affecting the splint bones, as a callosity or hard excrescence.
v. t.
Splint, or splent, coal. See Splent coal, under Splent.
n.
A piece that is split off, or made thin, by splitting; a splinter; a fragment.
a.
Habitually careful to agree with a standard, a rule, or a promise; accurate; methodical; punctual; as, a man exact in observing an appointment; in my doings I was exact.