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Topic: Abelian theorem

Related Topics

Abelian group

abelian categories

abelian varieties

free abelian group

finitely generated abelian groups

rank of an abelian group

abelian extensions

pre Abelian categories

category of abelian groups

Topological abelian group

arithmetic of abelian varieties

Abelian and tauberian theorems

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	PlanetMath: abelian group
		Theorem 1 Any subgroup of an abelian group is normal.
		Theorem 2 Quotient groups of abelian groups are also abelian.
		This is version 21 of abelian group, born on 2003-10-15, modified 2006-12-12.
	planetmath.org /encyclopedia/Abelian.html (198 words)

	PlanetMath: Abel summability
		Abel's theorem is the prototype for a number of other theorems about convergence, which are collectively known in analysis as Abelian theorems.
		An important class of associated results are the so-called Tauberian theorems.
		Ikehara's theorem is especially noteworthy because it is used to prove the prime number theorem.
	planetmath.org /encyclopedia/AbelianTheorem.html (393 words)

	Abelian and tauberian theorems - Wikipedia, the free encyclopedia
		In the abstract setting, therefore, an abelian theorem states that the domain of L contains convergent sequences, and its values there are equal to the Lim functional's.
		A tauberian theorem states, under some growth condition, that the domain of L is exactly the convergent sequences and no more.
		The development of the field of tauberian theorems received a fresh turn with Norbert Wiener's very general results, namely Wiener's tauberian theorem and its large collection of corollaries.
	en.wikipedia.org /wiki/Abelian_and_tauberian_theorems (552 words)

	Natural to Complex Numbers
		Theorem: The sum of a number (a, b) and its minus is the additive-identity; that is (a, b) + -(a, b) = -(a, b) + (a, b) = (a + b, a + b) = (1, 1) = 0.
		Theorem: An element a of the ring commutes with its additive inverse (- a); that is, we have a (- a) = (- a) a.
		Theorem: A vector v of V has a unique expression in terms of a given basis B of V. Theorem: Each basis of V has the same cardinality, which we call the dimension of V. Definitions: A geometry is said to be positive; if for every vector v in v, we have v.
	www.rism.com /Trig/natural_to_complex_numbers.htm (6128 words)

	Abel's theorem - Wikipedia, the free encyclopedia
		Abel's theorem is frequently useful in dealing with generating functions of real-valued and non-negative sequences, such as probability-generating functions.
		Converses to a theorem like Abel's are called Tauberian theorems: there is no exact converse, but results conditional on some hypothesis.
		Abelian theorem at PlanetMath; a more general look at Abelian theorems of this type.
	en.wikipedia.org /wiki/Abel's_theorem (319 words)

	SPRING SCHOOL ON ABELIAN VARIETIES
		After a short break (25 May 2006 is Ascension Day), the Spring School will be concluded by a 3-day Workshop on Abelian Varieties, to be held at the University of Amsterdam.
		The Spring School is organized by the Mathematics Research Institute (MRI) in the Netherlands, in collaboration with the Thomas Stieltjes Institute.
		There is a new textbook on Abelian Varieties in preparation by Gerard van der Geer and Ben Moonen.
	staff.science.uva.nl /~bmoonen/springsch/SprSch.html (476 words)

	McCune/Padmanabhan Monograph Problems (Site not responding. Last check: 2007-10-15)
		Theorem ABGT-2 Identity with (gL) is a commutative monoid.
		Theorem PIX-1 Inconsistency of Pixley polynomial with (gL).
		Theorem RBA-3 A Robbins algebra with c+d=c is Boolean.
	www-unix.mcs.anl.gov /~mccune/papers/monograph/problems.html (1178 words)

	[No title]
		Suppose the p-compact group X is abelian and f : Bß ____-BY is induced from a monomorphism.
		Suppose V is an elementary abelian p-group and T ____-Y is a maximal torus of a connected p-compact group Y with Weyl group W (Y).
		Conse- quently [8, Theorem 4.6] implies that (Y =X)hß is Fp-finite.
	hopf.math.purdue.edu /Ishiguro-LeeHS/2_21_02.txt (4028 words)

	[No title]
		The conclusion of Theorem 1 may be taken as a definition of the quantum ergodicity of a quantized abelian or G-abelian system.
		In the case of manifolds with diffractive boundary, Farris' extension of the Egorov Theorem (which is carried out from the $C^$ algebra point of view) is sufficient for the proof of quantum ergodicity using Theorem* 1.
		The composition theorem for Fourier Integral and Hermite operators [B.G.,\S7] shows that $$\sigma (\alpha ^H_t(\Pi A\Pi)) = \sa \circ G^t_\Sigma $$ where $G^t$ is the Hamilton flow of $\sigma _H$ on $\Sigma $.
	www.ma.utexas.edu /mp_arc/html/papers/95-264 (5733 words)

	Series of groups; solvable groups revisited
		We strongly advise the reader to prove the theorem (see exercise 3 for this section) using the initial definition (Definition 8.1.6) without making use of the equivalent characterization we have just established.
		Theorem 11.2.5 Any subgroup and any factor group of a solvable group is solvable.
		By Schreier's Theorem (Theroem 11.2.2), (11.7) and (11.10) have equivalent refinements.
	web.usna.navy.mil /~wdj/tonybook/gpthry/node63.html (689 words)

	Finitely generated abelian groups
		We will now prove the structure theorem for finitely generated abelian groups, since it will be crucial for much of what we will do later.
		Then we see that finitely generated abelian groups can be presented as quotients of finite rank free abelian groups, and such a presentation can be reinterpreted in terms of matrices over the integers.
		We obtain a proof of the theorem by reinterpreting in terms of groups.
	modular.fas.harvard.edu /129/ant/html/node9.html (725 words)

	[No title]
		Theorem 1* *.1 was previously known in the case p = 2 and E assumed to be 1-connected by work of Lannes and Schwartz [18], but was actually rediscovered independently by the author and formed the starting point for this work.
		Theorem 3.3 and 5.10 now implies that E has to be Fp equival* *ent to P2E, and furthermore that ss2(E) cannot contain p-torsion.
		Theorem 5.13 thus in particular shows that for the coho- mology of a finite Postnikov system, being of finite transcendence degree is eq* *uiva- lent to being noetherian.
	www.math.purdue.edu /research/atopology/Grodal/postnikov.txt (6592 words)

	Computing Papers on Theorem (Site not responding. Last check: 2007-10-15)
		Some of the principal Theorems include the existence of a universal program, the unsolvability of the halting problem (there does not exist a mechanical means of checking for infinite loops in the executions of programs), and Rice`s Theorem.
		The sweeping conclusion of Rice`s Theorem is the impossibility of algorithmically analyzing computer programs to determine in which cases a given property is possessed by the function computed by the program.
		Unfortunately, after GÂ¨del announced his famed incompleteness Theorem in o 1931 stating that it is impossible to have a formalism that can help us to reach all truths and only truths, we nally realized that we had gone a long way in ghting a battle that was impossible to win.
	computing.breinestorm.net /Theorem (3065 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		The necessary and sufficient condition for a Liouville type theorem to hold is that the real Fermi surface of the elliptic operator consists of finitely many points (modulo the reciprocal lattice).
		Thus, such a theorem generically is expected to hold at the edges of the spectrum.
		It is provided in Theorem 4.3.1 of \cite{Ku} for the case of periodic equations in $\RR^n$, however carrying it over to the case of more general abelian coverings does not present any difficulty.
	www.ma.utexas.edu /mp_arc/html/papers/05-91 (9553 words)

	[No title]
		When the hypothesis of the theorem holds we say that R and S are derived equivalent, and so the result says that derived equivalent rings have isomorphic K-theories.
		Using this result Neeman is able to prove Theorem C(b), and from this he is able to deduce Theorem B in the case of regular rings (because for regular rings one has G(R) ~=K(R)).
		This theorem cannot be extended to cover the case where R or S is a different* ial graded algebra; we give an example in [DS ] which is discussed a little in Rema *rk 6.8.
	hopf.math.purdue.edu /Dugger-Shipley/kdeqDS.txt (10785 words)

	[No title]
		One restriction employs the notion of an {\it algebraic integer}, which is a complex number that is a root of a monic polynomial in the polynomial ring $\mathbb{Z}[z]$.
		Then by Theorem \ref{char} and Theorem \ref{lift7}, \[ B\hat X=\hat R_*\hat X=\alpha\hat X. So, $\alpha$ is an eigenvalue of $B$ (and $\hat X$ is an eigenvector of $B$.) The characteristic polynomial of $B$ is an n-degree monic polynomial in $\mathbb{Z}[z]$: \[ z^n+d_{n-1}z^{n-1}+\dots +d_1z+d_0.
		The multiplier group $\rho_\phi(S_\phi)$ is Abelian because it is a subgroup of the Abelian group $\mathbb{R}^*$.
	www.maths.tcd.ie /EMIS/journals/EJDE/Volumes/Volumes/2004/39/bakker-tex (2562 words)

	[No title]
		Relating Cebotarev's density theorem for the 13th cyclotomic field to the distribution of primes mod 13.
		A finite abelian extension of K in C corresponds to a closed subgroup of ideles containing principal ideles and having finite quotient.
		Summary of infinite class field theory: an abelian extension of K in C corresponds to a closed subgroup of ideles containing principal ideles and having totally disconnected quotient.
	cr.yp.to /2000-515/inclass.html (3147 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		The results are also established for overdetermined elliptic systems, which in particular leads to Liouville theorems for polynomially growing holomorphic functions on abelian coverings of compact analytic manifolds.
		Consider a normal abelian covering\footnote{The word `covering' in this paper always means `normal covering'.} of a compact $d$-dimensional Riemannian manifold $M$ $$ X \mathop{\mapsto}\limits^{G} M, $$ where $G$ is the (abelian) deck group of the covering.
		Theorems \ref{T:Liouville} and \ref{T:Liouville_dim} imply now that the Liouville theorem holds, and every solution $u\in \mathrm{V}_N(L)$ is representable in the form (\ref{polyn}).
	www.ma.utexas.edu /mp_arc/papers/05-91 (9553 words)

	G
		On the decomposition of the convolution of a Gaussian and Poisson distribution on locally compact Abelian groups, J. of Mult.
		Theorems of Marcienkiewich's and Lukac's on Abelian groups, Teor.
		On a characterization of the Gaussian distribution on Abelian groups by constancy of regression, Teor.
	www.ilt.kharkov.ua /bvi/structure/depart_e/d25/feldman-pub_e.htm (622 words)

	[No title]
		Abelian groups ----------------------------------------------------------- State and prove the structure theorem for abelian groups.
		State the structure theorem for Modules over a PID, and how it applies to linear operators on a vector space.
		Structure theorem for semisimple algebras (Artin-Wedderburn.) State and prove Maschke's Theorem.
	www.math.princeton.edu /generals/algebra.txt (924 words)

	Citebase - On the non-Abelian Stokes theorem for SU(2) gauge fields
		Authors: Gubarev, F. We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required.
		We also derive the non-Abelian Stokes theorem on the lattice and discuss various terms contributing to the trace of the Wilson loop.
		The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral one, have been formulated in their simplest possible forms...
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:hep-lat/0309023 (1252 words)

	Journal of Formalized Mathematics, Index of MML Identifiers
		The Hahn Banach Theorem in the Vector Space over the Field of Complex Numbers.
		Graph Theoretical Properties of Arcs in the Plane and Fashoda Meet Theorem.
		The Steinitz Theorem and the Dimension of a Vector Space.
	www.mizar.org /JFM/mmlident.html (2155 words)

	Decomposing and Factoring Abelian Varieties
		By the Poincare reducibility theorem, every abelian variety is isogenous to a product of simple abelian subvarieties.
		The following commands use the elements of a commutative subring of endomorphisms to decompose a modular abelian variety A into a direct sum of abelian subvarieties by taking kernels (which are analogous to generalized eigenspaces).
		Decompose an abelian variety A using the commutative ring of endomorphisms generated by the space of homomorphisms R of A. DecomposeUsing(phi) : MapModAbVar -> SeqEnum
	www.math.lsu.edu /magma/text1326.htm (349 words)

	Abstract - Compton (Site not responding. Last check: 2007-10-15)
		In classical analysis, an Abelian theorem is one that states that if the power series expansion of an analytic function behaves nicely at its radius of convergence, then function itself behaves nicely as it approaches the radius of convergence.
		To make the converse of an Abelian theorem true, one generally needs to add some condition to the hypothesis.
		A Tauberian theorem is a corrected converse to an Abelian theorem.
	algo.inria.fr /seminars/sem91-92/compton.html (95 words)

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