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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
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
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
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
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
{\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
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
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
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
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
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
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
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
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)
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
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
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
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
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
{\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
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
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
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
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
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
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
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
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
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
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
disciplines, including molecular genetics, biochemistry, and microbiology. It is split across two articles: Glossary of cellular and molecular biology (0–L) lists
Glossary of cellular and molecular biology (M–Z)
Glossary_of_cellular_and_molecular_biology_(M–Z)
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
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
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
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
complementary primers. The exact temperature at which annealing occurs is strongly influenced by the length and specific sequence of the individual strands
Glossary of cellular and molecular biology (0–L)
Glossary_of_cellular_and_molecular_biology_(0–L)
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
Ongoing Formula One season
safety car being deployed; at the resulting restart Leclerc crashed at the exact same corner, bringing about a lengthy red flag while officials inspected
2026 Formula One World Championship
2026_Formula_One_World_Championship
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
Eukaryotes other than animals, plants or fungi
quantified. The exact temporal relationship between these proposed stages is currently impossible to determine. They merely represent the sequence of ecological
Protist
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
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
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
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
List of large explosions
contact with picric acid turned their skin yellow – were killed, though the exact number has never been established. An unknown number of people were injured
Largest artificial non-nuclear explosions
Largest_artificial_non-nuclear_explosions
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
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
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)
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
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)
Ninth season of American Horror Story
Vega to work with series veteran collaborator Kyle Cooper on the official sequence. Later that month, FX officially released the promo posters for the season
American_Horror_Story:_1984
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
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
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 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)
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
South (informally, JetBlue Park) in Fort Myers, Florida. JetBlue is an exact copy of Fenway, including a full-sized Green Monster. The Red Sox' mascot
Glossary_of_baseball_terms
American cable network
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
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
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
2023 video game
PlatinumGames Japanese: ファイナルファンタジーXVI, Hepburn: Fainaru Fantajī Shikkusutīn The exact fate of Clive and Joshua, as well as who authored the book seen in the post-credits
Final_Fantasy_XVI
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
Family of operating systems for IBM PC compatibles
and cannot be exchanged between different DOS versions in general, as the exact behaviour differs between different DOS versions. In very old versions of
DOS
Strategy board game, variant of Pachisi
track to the home area safely without being captured by another player. The exact location of the starting point may vary according to the version, but it
Aggravation_(board_game)
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
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
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
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
Tabular arrangement of the chemical elements
form. In particular, this supplanted Brauner's asteroidal hypothesis. The exact position of the lanthanides, and thus the composition of group 3, remained
Periodic_table
there is now a gap in the numbering sequence. Benedict: Antipope Benedict X (1058–1059) was kept in the numbering sequence. Boniface: Antipope Boniface VII
List_of_popes
Failed colony in North America (1584–1590)
18, 2019. Lawson, John (1709). A New Voyage to Carolina; Containing the Exact Description and Natural History of that Country: Together with the Present
Roanoke_Colony
of him to infiltrate the Massachusetts Academy so that Black Tom could exact vengeance on his cousin, Banshee, who was the headmaster of the academy
List of Marvel Comics characters: M
List_of_Marvel_Comics_characters:_M
Free online crowdsourced encyclopedia
have far more topics than can be covered by any printed encyclopedia. The exact degree and manner of coverage on Wikipedia is under constant review by its
Wikipedia
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
American musician (1942–2025)
hearing in his right ear. The issue was diagnosed as a nerve impingement. The exact cause remains unclear. Due to this infirmity, Wilson developed a habit of
Brian_Wilson
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
Unsolved murders of teenage girl and domestic worker
were conflicting media reports about the exact sequence of events, which was somewhat like this: Possible sequence of events according to CBI Joint Director
2008_Noida_double_murder_case
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
Arabic, Muslim, Sindhi
Split
Boy/Male
Hindu
Inside viewer, Spilt second
Boy/Male
Muslim
Split, Cleavage
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Momentary; Lord Rama's Ancestor; Spilt-second; Lord Vishnu
Boy/Male
Muslim
Strong, Solid, Firm, Sharp
Boy/Male
Hebrew
May Jehovah exalt. God prepares.
Boy/Male
Muslim/Islamic
Split Cleavage
Boy/Male
English
From the split meadow.
Boy/Male
Hindu
Inside viewer, Spilt second
Boy/Male
Arabic, Muslim
Strong; Solid; Firm; Sharp
Girl/Female
Hindu, Indian, Telugu
Motherly Love; Energetic Sprit
Boy/Male
Hindu, Indian
Exact; Alert
Girl/Female
Hindu, Indian
Momentary; Split Second
Boy/Male
Gujarati, Hindu, Indian
One who Lives Life Long; Gains Victory Within Splits
Boy/Male
American, Australian, Chinese, Hebrew, Jewish
Exalt; Praised; Son of Jacob and Leah
Boy/Male
Indian, Punjabi, Sikh
Exact Love
Girl/Female
American, Christian, Hebrew, Indian
Narrow Split of Land
Boy/Male
American, British, English
From the Split Meadow
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Always Winning; A Winner; Invincible; Unconquerable
Boy/Male
Tamil
Pitambari | பீதாஂபரீÂ
Good character
Boy/Male
Arabic, Muslim
Ardent; Longing
Girl/Female
Hebrew Spanish
May Jehovah add and give increase.
Male
English
Variant spelling of English Shamus, SHEAMUS means "supplanter."
Female
English
Variant spelling of English Katelin, KATELYN means "pure."
Girl/Female
Arabic, Muslim
She was the Daughter of Muhammad Bin Abdul Aziz Bin Ali Bin Hibbat Allah Bin Khuldoon; She Narrated Hadith
Boy/Male
Hindu
Pullannam
Boy/Male
Hawaiian American
Form of John.
Girl/Female
Tamil
Fairy queen, Ambition
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
SPLIT EXACT-SEQUENCE
n.
A piece that is split off, or made thin, by splitting; a splinter; a fragment.
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.
v. t.
A splint bone.
v. t.
A piece split off; a splinter.
v. i.
To part asunder; to be rent; to burst; as, vessels split by the freezing of water in them.
imp. & p. p.
of Slit
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.
To render pure or refined; to intensify or concentrate; as, to exalt the juices of bodies.
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.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
v. i.
To attend to a spit; to use a spit.
v. t.
To split into splints, or thin, slender pieces; to splinter; to shiver.
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.
v. t.
One of the small plates of metal used in making splint armor. See Splint armor, below.
imp. & p. p.
of Spit
v. t.
Splint, or splent, coal. See Splent coal, under Splent.
v. t.
To divide or separate into components; -- often used with up; as, to split up sugar into alcohol and carbonic acid.
v. t.
A disease affecting the splint bones, as a callosity or hard excrescence.
n.
To cut lengthwise; to cut into long pieces or strips; as, to slit iron bars into nail rods; to slit leather into straps.
imp. & p. p.
of Split