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Topic: Exact sequence

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exact sequence

exact functor

short exact sequence

Closed and exact differential forms

Signing Exact English

Exact trigonometric constants

long exact sequence

left exact

left exact functor

Exact coloring

Exact inexact arithmetic

Exact count

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	Exact sequence - Wikipedia, the free encyclopedia
		In mathematics, especially in homological algebra and other applications of Abelian category theory, as well as in group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them such that the image of one morphism equals the kernel of the next.
		When dealing with exact sequences of groups, it is common to write 1 instead of 0 for the trivial group with a single element.
		The five lemma gives conditions under which the middle map in a commutative diagram with exact rows of length 5 is an isomorphism; the short five lemma is a special case thereof applying to short exact sequences.
	en.wikipedia.org /wiki/Exact_sequence (1023 words)

	Sequence - Wikipedia, the free encyclopedia
		In mathematics, a sequence is a list of objects (or events) arranged in a "linear" fashion, such that the order of the members is well defined and significant.
		A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.
		If the terms of the sequence are a subset of a ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing.
	en.wikipedia.org /wiki/Sequence (631 words)

	Exact sequence
		To be precise, fix an Abelian category (such as the category of Abelian groups or the category of vector spaces over a given field) or some other category with kernelss and cokernels (such as the category of all groups).
		Dually, the sequence B → C → 0 is exact at C if and only if if the image of the map from B to C is all of C, i.e.
		Exact sequences are precisely those chain complexes whose homology is trivial.
	www.brainyencyclopedia.com /encyclopedia/e/ex/exact_sequence.html (1033 words)

	Exact functor
		Alternatively, one can argue that every short exact sequence of k-vector spaces splits, and any additive functor turns split sequences into split sequences.) If X is a topological space, we can consider the abelian category of all sheaves of abelian groups on X.
		The degree to which a left exact functor fails to be exact can be measured with its right derived functors; the degree to which a right exact functor fails to be exact can be measured with its left derived functorss.
		Left- and right exact functors are ubiquitous mainly because of the following fact: if the functor F is left adjoint to G, then F is right exact and G is left exact.
	encyclopedia.codeboy.net /wikipedia/e/ex/exact_functor.html (486 words)

	Bic Exact Tip (Site not responding. Last check: 2007-08-19)
		Exact sequence 2: y theory, as well as in group theory, an '''exact sequence''' is a (finite or infinite) sequence] 11: The sequence is ''exact '' at A_i if the 2.
		Closed and exact differential forms 4: ology, the concepts of '''closed form''' and '''exact form''' are defined for differential form s, b 14: for an exact form, with ''andalpha;'' given and ''andbeta;'' unkno 16: It makes no real sense to ask whether a 0-form is exact, since ''d'' increases degree by 1.
		Exact functor 3: of a short exact sequence into a three-term exact sequence 4: * '''left-exact ''' if it transforms kernel (category theory)ke 5: * '''right-exact ''' if it transforms cokernel s into cokernels 6: t, i.e.
	www.vermontreview.com /edge/32703-bicexacttip.html (593 words)

	[No title]
		This is a sequence_in general not exact_of groups and homomor- phisms that includes the Gottlieb groups of X and the evaluation subgrou* *ps of f.
		We show that the relevant long exact sequences of rational homotopy groups of function spaces are naturally expressed as homology exact sequences of derivations com- plexes of Sullivan minimal models.
		Y is a boundary sequence, but not usually an exact sequence, it is natural to consider its homology.
	hopf.math.purdue.edu /Lupton-SmithSB/Gseq.txt (15291 words)

	Exact functor (Site not responding. Last check: 2007-08-19)
		To check whether an additive functor is it is enough to check that it short exact sequences into short exact sequence.
		The degree to which a left exact fails to be exact can be measured its right derived functors ; the degree to which a right functor fails to be exact can be with its left derived functors.
		Left- and right exact functors are ubiquitous because of the following fact: if the F is left adjoint to G then F is right exact and G is left exact.
	www.freeglossary.com /Exact_functor (774 words)

	Summand of a Free Module
		A short exact sequence is split exact if there is a copy of c in b, which I will call d, and the homomorphism b → c maps d onto c.
		When a short exact sequence is split exact, b is a semidirect product, rather than a direct product.
		A module p is projective iff every short exact sequence ending in p is split exact, iff p is the summand of a free module.
	www.mathreference.com /mod-pit,summand.html (694 words)

	AMCA: On the exact sequence associated to a fibration of 2-groupoids by Enrico Vitale (Site not responding. Last check: 2007-08-19)
		One of the basic construction in algebraic topology is the homotopy long exact sequence of groups and pointed sets associated, for each point of the domain, to a Hurewicz fibration between two topological spaces.
		Recently, Hardie, Kamps and Kieboom have shown that, up to the dimension 2, this exact sequence is a special case of a 9-term exact sequence associated to a fibration of bigroupoids.
		Roughly speaking, the idea is the following : Brown associates a 6-term exact sequence of groups and pointed sets to a fibration of groupoids ; since a 2-groupoid is to be thought as a higher dimensional groupoid, we have to associate a sequence of "higher dimensional" groups and pointed sets to a fibration of 2-groupoids.
	at.yorku.ca /c/a/e/q/15.htm (342 words)

	PlanetMath: exact sequence
		Compare this to the notion of a chain complex.
		Cross-references: chain complex, adjacent, sequence, kernel, image, modules, category, homomorphisms
		This is version 2 of exact sequence, born on 2002-01-05, modified 2002-05-01.
	planetmath.org /encyclopedia/ExactSequence.html (67 words)

	ipedia.com: Homology (mathematics) Article
		In mathematics, homology is a certain general procedure to associate a sequence of abelian groups or modules to a given mathematical object.
		In mathematics (especially algebraic topology and abstract algebra), homology is a certain general procedure to associate a sequence of abelian groups or modules to a given mathematical object (such as a topological space or a group).
		A chain complex is said to be exact if the image of the n+1-th map is always equal to the kernel of the n-th map.
	www.ipedia.com /homology__mathematics_.html (770 words)

	[No title]
		Because the spectral sequence is as Hopf algebras we know that a differential must originate on a generator in filtration 2 or hi* *gher and hit a primitive ([Smi70, page 78].
		Since the kernel is polynomial we see that for SO the spectral sequence collaps* es to CK1 E. CK1 is the cokernel in filtration 0 and E is Tor of the kernel which is polynomial and so the exterior generators are in filtration one and have tri *vial differentials.
		The exact sequences of Theorem 1.5 don't allow us to address the map on BP to the fibre but we have now managed to see that it is what we would expect it to be anyway.
	hopf.math.purdue.edu /Kitchloo-Laures-Wilson/kitchloo-laures-wilson.txt (10880 words)

	Citebase - Rationalized Evaluation Subgroups of a Map and the Rationalized G-Sequence
		The G-sequence of a map f : X → Y is a sequence · · · → Gn (X) → Gn (Y, X; f) → Grel (Y, X; f) → Gn−1 (X) → · · · n of groups and homomorphisms that derives from the long exact homotopy sequence of the map f.
		In this sequence, Gn (X) is the Gottlieb group of X, Gn (Y, X; f) is rel the evaluation subgroup of f introduced above, and the third term Gn (Y, X; f) is a suitably defined "relative" term.
		We show that several related long exact sequences of rational homotopy groups are naturally expressed as long exact sequences in homology of derivation complexes of Sullivan minimal models.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0309432 (5348 words)

	A Restriction of Scalars Exact Sequence
		is geometrically connected, we base extend the exact sequence (2.1) to
		7.5.3 (a)] asserts that the sequence tex2html_wrap_inline$0 &rarr#rightarrow;A_Z_q &rarr#rightarrow;R_Z_q &rarr#rightarrow;E_Z_q$is exact.
		We use that formation of Néron models commutes with unramified base extension and check exactness of (2.2) after base extension to the unramified extension tex2html_wrap_inline$O_K,q$ of tex2html_wrap_inline$Z_q$.
	modular.fas.harvard.edu /papers/nonsquaresha/nonsquaresha/node5.html (379 words)

	Citebase - A long exact sequence for symplectic Floer cohomology
		The long exact sequence describes how the Floer cohomology of two Lagrangian submanifolds changes if one of them is modified by applying a Dehn twist.
		The paper contains a certain amount of material that may be of interest independently of the exact sequence: in particular, chapter 1 covers "symplectic Picard-Lefschetz theory" in some detail, and chapter 2 contains a generalization of the usual TQFT setup for Floer cohomology.
		We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0105186 (1027 words)

	Creating High-Impact Documents
		A standard feature of the GIF image format is the option to store the image data in the GIF file in an interlaced fashion: instead of storing the image's scan lines in exact sequence, equally spaced nonadjacent sets of lines are stored together, and these sets are stored in sequence.
		JPEG is also a "lossy" compression method, meaning that you don't generally get the exact same image data upon decoding that you had when you encoded the image.
		Here is a document that consists of the above four examples in sequence, followed by lots and lots of plain text.
	wp.netscape.com /assist/net_sites/impact_docs/index.html (1361 words)

	AllRefer.com - Sennacherib (Ancient History, Middle East, Biography) - Encyclopedia
		B.C. The son of Sargon, Sennacherib spent most of his reign fighting to maintain the empire established by his father.
		It is difficult to determine the exact sequence of his conquests, but his first campaign seems to have been waged against Babylonia.
		B.C. The exact outcome of the battle is uncertain.
	reference.allrefer.com /encyclopedia/S/Sennache.html (317 words)

	A Long Exact Sequence for the Branching Homology (ResearchIndex) (Site not responding. Last check: 2007-08-19)
		Abstract: A function complex is introduced on the category of flows so that the model category of ows becomes a simplicial model category.
		The crux of the proof is that the homotopy branching space of the terminal flow is contractible.
		We then easily deduce a long exact sequence for the branching homology of a flow.
	citeseer.ist.psu.edu /593769.html (385 words)

	Normal transversality
		Lemma 2.2 Let A be a commutative ring, I, J two ideals of A and M an A-module.
		Clearly it is an exact sequence of A-modules.
		The following is a commutative diagram of exact columns with rows the last three nonzero terms of the complexes
	www-ma1.upc.es /recerca/preprints/99/9902planas/node2.html (417 words)

	Calendars - Numericana
		The exact day when an heliacal rising is observed may depend on the longitude and latitude of the observer.
		The exact sequence of the different types of years is determined by 4 so-called rules of postponement (dehioth, dehiyyot) whose purpose is to prevent the celebration of some of the above festivals on certain days of the week.
		The Mayan civil year, the haab consisted of 18 "months" (uinals), of 20 days each, and 5 extra days (which were believed to be unlucky ones), for the same total of 365 days as the Egyptian year.
	home.att.net /~numericana/answer/calendar.htm (8129 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations.
		We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super Korteweg-de Vries (KdV) hierarchy.
		We combine this algebraic approach with an analytic analysis of the super heat operator.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20547065 (305 words)

	PlanetMath: exact sequence
		Cross-references: sequence, epimorphism, monomorphism, kernel, cokernel, factors, image, morphism, abelian category
		This is version 5 of exact sequence, born on 2002-04-24, modified 2005-03-15.
		(Category theory; homological algebra :: Abelian categories :: Exact categories, abelian categories)
	planetmath.org /encyclopedia/ExactSequence2.html (78 words)

	split exact sequence - OneLook Dictionary Search (Site not responding. Last check: 2007-08-19)
		We found one dictionary with English definitions that includes the word split exact sequence:
		Tip: Click on the first link on a line below to go directly to a page where "split exact sequence" is defined.
		Split Exact Sequence : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=split+exact+sequence (75 words)

	Esophageal function tests
		The esophagus is a long, muscular tube that also has two muscles (or sphincters) at the top and bottom.
		All of these muscular areas must contract in an exact sequence for swallowing to proceed normally.
		There are three main symptoms that occur when esophageal function is abnormal: difficulty with swallowing (dysphagia), heartburn, and chest pain.
	www.healthatoz.com /healthatoz/Atoz/ency/esophageal_function_tests.jsp (1392 words)

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