
	Where results make sense

Topic: Cokernel algebra

Related Topics

abstract algebra

algebraic geometry

linear algebra

algebraic topology

Boolean algebra

Lie algebra

algebraic varieties

basis linear algebra

ring algebra

associative algebra

algebraic notation

homological algebra

In the News (Fri 10 Jul 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Cokernel - Wikipedia, the free encyclopedia
		In many situations in abstract algebra, such as for abelian groups, vector spaces or modules, the cokernel of the homomorphism f : X → Y is the quotient of Y by the image of f.
		The cokernel of a morphism f : X → Y is defined as the coequalizer of f and the zero morphism 0
		In the category of groups, the cokernel of a group homomorphism f : G → H is the quotient of H by the normal closure of the image of f.
	en.wikipedia.org /wiki/Cokernel (522 words)

	Kernel (category theory)
		Kernels are familiar in many categories from abstract algebra, such as the category of groups or the category of (left) modules over a fixed ring (including vector spaces over a fixed field).
		That is, the kernel of a morphism is its cokernel in the opposite category[?], and vice versa.
		Universal algebra defines a notion of kernel for homomorphisms between two algebraic structures of the same kind.
	www.ebroadcast.com.au /lookup/encyclopedia/ke/Kernel_of_a_morphism.html (781 words)

	[No title]
		Quillen's theorem for unipotent algebraic groups It is by now a wellknown fact that the dual of the (reduced) Steenrod alge- bra A* is isomorphic to the coordinate algebra of the (infinite dimensional) group scheme G = Aut s(Fa(x; y)) of the strict automorphism of the additive formal group law defined over Fp.
		The algebra of (reduced) mod p unstable cohomology cooperations is a polynomial algebra P pi B* = Fp[0; 1; : :]:with comultiplication 4n = n-i i.
		Wilkerson, The cohomology algebras of finite dimensional Hopf algebras, Trans.
	www.math.purdue.edu /research/atopology/PetersonC/Ext_An.txt (2570 words)

	Complexes of Modules
		The homology of the complex in degree n is the quotient of the kernel of the n^(th) boundary map by the cokernel of the boundary map of degree n - 1.
		Given a complex C of modules over a basic algebra, returns the complex of length one greater that is obtained by adjoining the zero map from the zero module to the term of highest degree in the complex.
		Given a complex C of modules over a basic algebra, returns the complex of length one greater that is obtained by adjoining the zero map to the zero module from the term of lowest degree in the complex.
	www.math.lsu.edu /magma/text797.htm (1807 words)

	Lucian Ionescu's Stuff
		Interpreting the elements of a non-associative algebra as "vector fields" and the multiplication as a connection, we investigate a natural candidate for the algebra of functions, with derivations the former algebra.
		The associator of a non-associative algebra is the curvature of the Hochschild quasi-complex.
		Conditions for the existance of an ``algebra of functions'' having as algebra of derivations the original non-associative algebra, are investigated.
	www.ilstu.edu /~lmiones/research.htm (1098 words)

	PlanetMath: supplemental axioms for an Abelian category
		Every monic is the kernel of its cokernel.
		Grothendieck introduced these in his homological algebra paper Sur quelques points d'algèbre homologique in the Tôhoku Math Journal (number 2, volume 9, 1957).
		This is version 7 of supplemental axioms for an Abelian category, born on 2001-12-12, modified 2004-04-07.
	planetmath.org /encyclopedia/Complete8.html (222 words)

	Homomorphisms (Site not responding. Last check: 2007-10-24)
		Given an element x in a module over a basic algebra and a natural number n, the function returns the homomorphism from the n^(th) projective module for the algebra to the module with the property that the idempotent e of the projective module maps to x * e.
		The cokernel of f and the quotient map from cs{Codomain(f)} onto the cokernel.
		In particular, we choose the group algebra of an extra special 3-group and factor out the ideal generated by (z - 1)^2 where z is a central element of order 3.
	www.sci.kuniv.edu.kw /magma/text739.html (1385 words)

	[No title]
		B is a degreewise split inclusion whose cokernel C is a complex of relative projectives.
		Conversely, suppose that i is a degreewise split monomorphism and the cokernel C of i is P-cofibrant.
		In addition to the connection between phantom maps and pure homological algebra, the authors are interested in the pure derived category as a tool for connecting the global pure dimension of a ring R to the behaviour of phantom maps in DC and DP under composition.
	jdc.math.uwo.ca /papers/relative.txt (10317 words)

	[No title]
		One's first reaction mig* ht be that because the continuous cohomology of a profinite group is the colimit of the co homology of finite groups, the profinite case should be a direct consequence of the finite *case by passing to appropriate (co-)limits.
		Furthermore HK is a Poincare duality algebra* of dimension 3 and as * a Z=3 module H1K ~= (F3)2 is isomorphic to the augmentation ideal I(Z=3) in the group * algebra F3[Z=3].
		Now consider the graded Lie algebra a* ssociated to the decreasing filtration of SL(2; Z3) by the kernels of mod 3k reduction, k = 1; 2; : :.:It is easy to see from this Lie algebra, say as in the proof of 4.4, that H1K ~=(F3)3 *.
	hopf.math.purdue.edu /Henn/profin.txt (11132 words)

	Chain Maps (Site not responding. Last check: 2007-10-24)
		Returns the cokernel complex of f and the projection of the cokernel onto the codomain of f.
		We from the basic algebra of the direct product of a cyclic group of order 3 with symmetric group on three letters over the field with three elements.
		The long exact sequence on homology for the exact sequence of complexes given by the chain maps f and g as a chain complex with the homology group in degree i for the Cokernel of the complex C appearing in degree 3i.
	www.sci.kuniv.edu.kw /magma/text744.html (1362 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-24)
		In algebra an incomplete list of them includes linear substitutions in systems of linear equations, and multiplication of quaternions and elements of a Grassmann algebra; in analytic geometry it includes coordinate transformations; in analysis it includes differential and integral transforms and the Fourier integral.
		To algebraic operations on linear operators correspond operations of the same name on their matrices, taken in fixed bases.
		Results that are in a certain sense close to final have been obtained by methods of homological algebra [5].
	eom.springer.de /L/l059340.htm (3235 words)

	L.L. Avramov Abstract (Site not responding. Last check: 2007-10-24)
		This condition can be restated in terms of linear algebra over the ring $R$ of algebraic functions vanishing on $X$: The cokernel $\Omega_{R\bold C$ of the linear map $R^r\to R^n$ induced by $J$ is projective, that is, splits off as a direct summand of $R^n$.
		Once the algebraic nature of $\Omega_{R\bold C$ was realized (in the fifties), functorial constructions of a module of Kahler differentials $\Omega_{R\bold k}$ were proposed for each commutative algebra $R$ over any commutative ring $\bold k$.
		In a familiar to mathematicians reversal of roles, the conclusion of the classical theorem was taken as a definition of smoothness for (some) algebras.
	www.math.uiuc.edu /Colloquia/99SP/avramov.html (207 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		This research is concerned with a number of questions in commutative algebra and algebraic geometry.
		Algebraic geometry studies solutions of families of polynomial equations.
		One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring.
	www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9322556.txt (126 words)

	UBC Algebra/Topology Seminar (Site not responding. Last check: 2007-10-24)
		The Iwasawa algebra is the power series ring in one variable over the p-adic integers (p a fixed prime).
		It has long been studied by number theorists in connection with Z_p-extensions of number fields.In particular, there is a beautiful classification theorem for finitely-generated modules over it that has been exploited to great advantage.
		The Iwasawa algebra also arises in homotopy theory, as a ring of Adams operations on p-adic complex K-theory.
	www.math.ubc.ca /~scull/smabs.html (163 words)

	Snake lemma - ExampleProblems.com
		In mathematics, particularly homological algebra, the snake lemma, a statement valid in every Abelian category, is the crucial tool used to construct the long exact sequences that are ubiquitous in homological algebra and its applications, for instance in algebraic topology.
		Then there is an exact sequence relating the kernels and cokernels of a, b, and c:
		The maps between the kernels and the maps between the cokernels are induced in a natural manner by the given (horizontal) maps because of the diagram's commutativity.
	www.exampleproblems.com /wiki/index.php/Snake_lemma (513 words)

	[No title]
		The E cohomology of Eilenberg-Mac Lane spaces was algebraically determined in [RWY98, Theorem 1.14].
		The bottom one is split as algebras and is part polynomial and sometimes has the Morava K-theory of an Eilenberg-Mac Lane space in it (to be identified soon).
		We work with topologized algebras and so the cokernel of algebr* as must have a topology on it and it is possible to put a topology on it so that i t is not the cokernel* stated in our Theorem 6.8.
	www.math.purdue.edu /research/atopology/Kashiwabara-Wilson/kash-wil.txt (17545 words)

	ellery kind (Site not responding. Last check: 2007-10-24)
		In abstract algebra, the cokernel of a homomorphism f X Y is the quotient set of Y by the image of f.
		The cokernel of a morphism f X Y is defined as the coequalizer of f and the zero morphism 0
		In the category of groups, the cokernel of a group homomorphism f G H is the quotient group of H by the normal closure of the image of f.
	elleryfdog.blogspot.com (11299 words)

	[No title]
		We use Hilbert module language to study the semi-invariant subspaces of a family of weighted Fock spaces and their quotients that includes the Full Fock space, the symmetric Fock space, the Direichet algebra, and the reproducing kernel Hilbert spaces with Nevanlinna-Pick kernel.
		In viewing contraction operators on a Hilbert space as contractive Hilbert modules over the disk algebra, the Sz.-Nagy-Foias canonical model can be seen to correpond to a short exact resolution of the given module by isometric modules.
		While in commutative algebra, there is a connection between the Euler charateristic of an algebraic Koszul complex and the Samuel multiplicity.
	www.math.tamu.edu /research/workshops/linanalysis/speakers.html (1057 words)

	preadditive categories are all Abelian - Page 2
		An exact category is an additive category eqiupped with extra structure: a class of pairs of morphisms (i,p) where i is an inflation and p a deflation.
		i is a kernel of p and p a cokernel of i and a load of other properties too.
		As for the sheaves thing: the kernel or cokernel, whichever one it is is certainly a presheaf, that is on each open patch we can take (co)kernels but they do not necessarily patch together to give a global section.
	www.physicsforums.com /showthread.php?t=100503&page=2 (560 words)

	Citations: Homotopical algebra in homotopical categories - Grandis (ResearchIndex)
		Following his approach, the discrete cat groups D(1 (G) Ker(1 G) 1 is the cat group with a single arrow) is the object of loops Omega Gamma G) so that 1 (G) 0(Omega Gamma G) Moreover, the cat....
		1) Cf is the h cokernel of f, or standard homotopy cokernel, or mapping cone; # denotes....
		The abstract frame we will use for categories with homotopies is a notion of homotopical category, developed in previous papers and recalled in Subsections 1.1, 1.2: it is a sort of lax 2 category with suitable comma and cocomma squares.
	citeseer.ist.psu.edu /context/893350/0 (943 words)

	Univ at Albany: Math: W. F. Hammond: Courses: Math 520B
		Any finitely-generated module of finite rank over a PID R may be realized, up to isomorphism, as the cokernel of a an R-linear map R^{n} ----> R^{m}, hence as the cokernel of the R-linear map associated with an m \times n matrix in R. A good computer algebra system is an indispensible aid.
		From the normal form one may read off that the cokernel of M is isomorphic to Z/3Z \times Z.
		M may be regarded as a rational matrix, and the associated Q-linear map is an automorphism of Q^{3}.
	nyjm.albany.edu:8000 /math/pers/hammond/course/mat520b/assgt/aah051121.html (168 words)

	Cohomology
		Given a projective resolution P for a simple module S over a basic algebra A, the function returns the chain maps in compact form of a minimal set of generators for the cohomology Ext_A^ * (S, S).
		Here are the ranks as free modules over the group algebra of the terms of the projective resolution of the trivial module cs{s}.
		We create the Basic algebra for the principal block of the sporadic simple group M_(11) in characteristic 2.
	www.umich.edu /~gpcc/scs/magma/text1010.htm (659 words)

	preadditive categories are all Abelian
		In both, it mentions how to construct a map whose kernel and cokernel are both zero, but is not an isomorphism.
		For vector bundles anyway, I think the point is that the pointwise kernel and cokernel may not have constant dimension, and therefore they do not comprise a bundle.
		I read something like this: the category of vector bundles is equivalent to the category of finitely generated locally free OX-modules, where OX is the sheaf of functions (this looks very similar to Swan's theorem).
	www.physicsforums.com /showthread.php?p=833015 (1572 words)

	Contents of Introduction (Site not responding. Last check: 2007-10-24)
		(that is, either an algebraic number field or an algebraic function field in one variable over a finite constant field) the structure of the Brauer group
		In the 1960s and 1970s, turning the cohomological crank on the engine of Algebraic Geometry, Grothendieck, M. Artin and Mumford derived exact sequences for the Brauer group of function fields for varieties of dimension 1 and 2.
		Before proving Theorem 1.1, we review the theory underlying the definition of the ramification divisor of a division algebra.
	www.math.fau.edu /ford/preprints/darff/node1_ct.html (512 words)

	Categories and Functors (Site not responding. Last check: 2007-10-24)
		This section is intended to give (and hence fix) some notations as well as definitions.
		We will define various familiar looking terms (like injective, surjective morphisms, subobject, kernel, cokernel etc.) in context of any general category.
		We can define kernel and cokernel of a morphism in case of additive category.
	www.imsc.res.in /~sgautam/main/node2.html (550 words)

	Hida: $p$-adic ordinary Hecke algebras for ${\rm GL}(2)$
		We prove the control theorem and the independence of the Hecke algebra from the weight.
		Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and
		As for a size of the algebra, we make a conjecture which predicts the Krull dimension of the Hecke algebra.
	www.numdam.org /numdam-bin/item?id=AIF_1994__44_5_1289_0 (260 words)

	The Associated Complex Torus
		Let M be a space of cuspidal modular symbols, which is the kernel of an ideal in the Hecke algebra.
		The cyclic subgroup of the complex torus attached to M that is generated by the image under the period map of the modular symbol x.
		The period map attached to M is a linear map (AmbientSpace(M)) -> C^d, where d is the dimension of the space of modular forms associated to M. The cokernel of the period map is a complex torus A_M(C).
	www.math.niu.edu /help/math/magmahelp/text1063.html (1502 words)

	Graduate Courses
		Prerequisite: MTH 420 and MTH 430, or consent of instructor
		Algebraic number fields: finiteness of the class number, Dirichlet unit theorem, splitting of prime ideals in an extension field, ramification.
		Algebraic varieties with specialization to curves and surfaces, Riemann-Roch theorem.
	www.math.buffalo.edu /gr_course_list.html (2399 words)

	Math 251 Algebra Fall 2002
		The notions of cokernel and exact sequence were perhaps mentioned once each in the course.
		Topics which might conceivably be treated in Math 251, but which were not covered in fall 2002.
		Multiplicative systems in a ring and a treatment of localization which is adequate for a commutative algebra course.
	www.math.duke.edu /faculty/schoen/alg2002home.html (393 words)

Try your search on: Qwika (all wikis)