Where results make sense

About us   |   Why use us?   |   Reviews   |   PR   |   Contact us

Topic: Torsion-free

    Note: these results are not from the primary (high quality) database.

Ads by Google

Related Topics

Fundamental group

History of the separation axioms

First category

Zariski topology

Christian left

Baire category theorem

Calvin and Hobbes

In the News (Thu 17 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

Free abelian group - Wikipedia, the free encyclopedia All free abelian groups are torsion-free, and all finitely generated torsion-free abelian groups are free abelian. Note a point on terminology: a free abelian group is not the same as a free group that is abelian; in fact the only free groups that are abelian are those of rank 0 (the trivial group) and rank 1 (the infinite cyclic group). In abstract algebra, a free abelian group is an abelian group that has a "basis" in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients. en.wikipedia.org /wiki/Free_abelian_group   (641 words)

Torsion subgroup: Definition and Links by Encyclopedian.com - All about Torsion subgroup Every free [* Ma#Abelian-group#abelian[?] group *] is torsion free, but the converse is not true, as is shown by the additive group of the rational numbers Q. An abelian group G is torsion free if and only if it is flat[?] as a Z-module, which means that whenever K is a subgroup of the abelian group H, then the natural map between the tensor products K ⊗ G and H ⊗ G is injective. In group theory, the torsion subgroup of an abelian group G is the subgroup T of G which consists of all elements of G which have finite order. www.encyclopedian.com /to/Torsion-subgroup.html   (528 words)

Lee Lady: Finite Rank Torsion Free Modules over Dedekind Domains (a book) The theory of finite rank torsion free abelian groups is full of results that depend on countability, or on having characteristic zero, or working over a ring whose quotient field is a perfect field, as well as proofs using quite specialized results from number theory. Unlike the theory of torsion groups, the theory of finite rank torsion free modules is becoming something that fits in fairly well with the mainstream of commutative ring theory. And one becomes more aware of the fact that the theory of finite rank torsion free abelian groups is moving away from abelian group theory in general in much the same fashion that abelian group theory has moved away from general group theory. www.math.hawaii.edu /~lee/book   (629 words)

lecture12.html Corollary.} {Over a PID a finitely generated module $_RM$ is torsion free iff it is free.} {\bf Proof.} We may assume that $M\not= 0$ is torsion free. Therefore, since $a\not= 0$ and $M$ is torsion free, the map $\lambda_a:x\longmapsto ax$ is a monomorphism $\lambda_a:M\longrightarrow F$. Lemma.} {For every module $M$, $M_t$ is a (torsion) submodule and $M/M_t$ is torsion free.} {\bf Proof.} Suppose that $x, y \in M_t$. darkwing.uoregon.edu /~anderson/math648/lecture12.html   (1662 words)

BACKGROUND It is known that the first part of this algorithm (reducing a given free word to a free word of minimal possible length by "elementary" Whitehead automorphisms) is pretty fast (of quadratic time with respect to the length of the word). An outer automorphism $\Phi$ of a free group $F$ of finite rank is said to be reducible if there is a free factorization $F=F\sb 1 \star \cdots\star F\sb k\star F'$ such that $\Phi$ permutes the conjugacy classes of the subgroups $F\sb 1,\cdots,F\sb k$; otherwise, $\Phi$ is irreducible. Several fragments of the elementary theory of a free group of finite rank were shown to be decidable. www.cs.gc.cuny.edu /~cryptlab/gworld/problems/Back.html   (5364 words)

Torsion Torsion free connections are considered most frequently - the Levi-Civita connection is assumed to have zero torsion, for instance. Torsion is also sometimes used for the medical condition commonly known as bloat. Some topological invariants are called torsions: for example the Reidemeister-Schreier torsion of a group acting on a finite complex; and also the analytic torsion defined using Laplacians. www.worldhistory.com /wiki/T/Torsion.htm   (426 words)

Suspension support structure being free from torsion and pinch - Patent 4779855 Since no torsion and pinch are found in the elastic body of the first support means, the spring property of the elastic body is not changed and the characteristics of the vehicle may be held at a set condition. However, torsion and pinch such as to deform both elastic bodies about an axis of a piston rod act on both elastic bodies through spring reaction transmitted to the spring seat in bound and rebound of a wheel. 4, the elastic body 30 at the time of bounding and rebound is prevented from torsion and pinch by the spherical bearing 32 of the first support means 18. www.freepatentsonline.com /4779855.html   (2358 words)

RMK articles : Chirality and Helicity vs Topological Spin and Topological Torsion The distinct concept of Helicity is to be associated with the third rank tensor field of Topological Torsion induced by the interaction of the 4 vector potentials and field intensities (E, B). However, when the 4-divergence of Topological Torsion is not zero, the second Poincare invariant, E · B, is not zero, and parity is not conserved. On space-time domains where either Poincare Invariant is zero, the closed integrals of the Spin (respectively, Torsion) have values whose ratios are rational. www22.pair.com /csdc/pd2/pd2fre52.htm   (462 words)

Talk:Torsion - Wikipedia, the free encyclopedia I am quite sure that torsion is T = ((r` x r``) * r```) / ((r` x r``)^2) So the denominator is square. All text is available under the terms of the GNU Free Documentation License (see Copyrights for details). It may be a fine link to a paper in Gauge Theory of Gravity (or not, I didn't check, and I'm not sure whether I'm fit to judge), but it obviously doesn't clarify Torsion as mathematical concept. www.wikipedia.org /wiki/Talk:Torsion   (233 words)

ab_gps Something as simple as the group of rational numbers already shows 'torsion-free' is more general than 'free'. These completely characterize the group up to isomorphism _if_ the group is countable and contains no copy of what you call A_p/Z (the direct limit of the cyclic groups Z/(p^k Z).) I don't really think there is a good characterization of torsion-free abelian groups. The torsion subgroup is in turn a direct sum of its p-primary subgroups. www.math.niu.edu /~rusin/known-math/99/ab_gps   (613 words)

split-abel It must be torsion free, but the example of G/T = additive group of the rationals shows that it need not be. It must be torsion >free, but the example of G/T = additive group of the rationals >shows that it need not be. The torsion subgroup is the set of sequences of elements in these groups for which the order of the terms in the sequence stays bounded. www.math.niu.edu /~rusin/known-math/94/split-abel   (1283 words)

DC MetaData pour: The group of fractions of a torsion free lcm monoid is torsion free The group of fractions of a torsion free lcm monoid is torsion free DC MetaData pour: The group of fractions of a torsion free lcm monoid is torsion free Inparticular, the fact that Artin braid groups are torsion free now follows from Garside\'s results almost immediately. math-sahel.ujf-grenoble.fr /prepub-ccsd/ccsd-00000852.html   (88 words)

Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations While the interactions of both graviton and torsion in the bulk are controlled by the Planck mass, an additional exponential suppression comes for the torsion zero-mode on the visible brane. The massive torsion modes, on the other hand, are correlated with the corresponding gravitonic modes and may be detectable in TeV-scale experiments. This may serve as a natural explanation of why the effect of torsion is so much weaker than that of curvature on the brane. www.osti.gov /energycitations/product.biblio.jsp?osti_id=20443379   (255 words)

Moduli spaces for torsion free modules on curve singularities I - Greuel, Pfister (ResearchIndex) Greuel, G.-M.; Pfister, G.: Moduli spaces for torsion free modules on curve singularities. Abstract: this article is to construct coarse moduli spaces for torsion free R-modules or, which amounts to the same, for Cohen-Macaulay representations of R. (Update) in the local case of torsion free modules on curve singularities. citeseer.ist.psu.edu /greuel93moduli.html   (437 words)

modulesoverpids.doc Since a free module is torsion-free, the intersection of F and Mtor is 0. In particular, if n=1, K=(g) is torsion free since Rn is. Thus g itself is in this case a linearly independent generating set. Then F is a free submodule of M. Let m be an element of M. Suppose that the image of m in N is r1n1+ +rtnt. www.math.ucla.edu /~blasius/110bh.1.01w/modulesoverpids.doc   (1101 words)

Bibliography for Torsion Free Groups Murley, The classification of certain classes of torsion free abelian groups, Pac. M.C.R. Butler, A class of torsion free groups of finite rank, Proc. Arnold, A duality for torsion free modules of finite rank over a discrete valuation ring, Proc. www.math.hawaii.edu /~lee/book/ref.html   (367 words)

torsion In this case the torsion would not be zero. In some other theories of gravity there is torsion. But there's no experimental evidence for torsion, so most people stick with GR. math.ucr.edu /home/baez/gr/torsion.html   (413 words)

FreeFixedTorsionWaves.html The waves will reflect off the far end of the grill in either a free or fixed end fashion but the difference is difficult to see unless the students know what to look for exactly. This experiment consists of a metal grill that can be twisted to create torsion waves. www.phys.ufl.edu /demo/3_OscillationsWaves/B_WaveMotion/FreeFixedTorsionWaves.html   (50 words)

Finitely Generated and Torsion Free is Free Because m is torsion free, the kernel of this homomorphism is 0. Note, Q is an infinitely generated torsion free Z module that is not free. Let r be a pid and let m be a torsion free r module. www.mathreference.com /mod-pid,fgtf.html   (216 words)

DC MetaData for: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion We obtain an expression for the Reidemeister torsion of the mapping torus of the dual This means that the Reidemeister torsion counts the fixed point classes of all iterates In section 6.3 we establish a connection between the Reidemeister torsion of a mapping torus, www.esi.ac.at /Preprint-shadows/esi539.html   (610 words)

Torsion - index page - Free MP3 downloads, CDs, Bio Info, Tour Dates, Lyrics and More!" Torsion - index page - Free MP3 downloads, CDs, Bio Info, Tour Dates, Lyrics and More!" Torsion is a four piece Rock / Industrial band based out of the Philadelphia Suburbs. Then you will be up to date on all Torsion shows and news. artists.iuma.com /IUMA/Bands/Torsion   (134 words)

Discounted or Free by DiscountedorFree.com Claim your free iPod nano music player in 3 simple steps, participate in one offer, refer some friends and then claim your brand new iPod. Regularly updated and completely free to use, why not register for our regular and exclusive newsletter DiscountedorFree Direct. Browse a directory of the UK's best free offers, competitions, discounts, free samples and much more. www.discountedorfree.co.uk   (126 words)

adidas Women's Torsion Open Shoe - Free Shipping Free shipping to ALL 50 states, see details. UPS Ground shipping is FREE on all orders to the 48 contiguous states. If the billing address and shipping address on your order do not match, or if your billing information does not match the information on file with your credit card, there may be a delay in processing and shipping your order. www.shoes.com /product.asp?p=5007405~WomensAthletic&variant_id=37409   (294 words)

Torsion defination of Torsion. What is Torsion? Meaning of Torsion. What does Torsion mean? an instrument for estimating very minute forces, as electric or magnetic attractions and repulsions, by the torsion of a very slender wire or fiber having at its lower extremity a horizontal bar or needle, upon which the forces act. a scale for weighing in which the fulcra of the levers or beams are strained wires or strips acting by torsion. www.question.com /dictionary/torsion.html   (297 words)

Torsion, Order Ideal It is zero iff c is torsion free. A module is torsion free if it has no torsion elements, and torsion if it equals its torsion submodule. If h(c) is torsion then c maps into the kernel, which is torsion, hence c is torsion. www.mathreference.com /mod-pid,torord.html   (333 words)

CARAT Introduction / Examples / Find all Z-classes, affine classes and torsion free space groups in a given Q-class We see that there are 4 torsion free space groups. Find all Z-classes, affine classes and torsion free space groups in the Q-class of min.108. CARAT Introduction / Examples / Find all Z-classes, affine classes and torsion free space groups in a given Q-class wwwb.math.rwth-aachen.de /carat/examples/Ex12.html   (198 words)

tfodd.txt It is an interesting problem to consider which infinite loop s* *paces have 2-torsion free homology, and what limits that assumption puts on the torsi* *on in homotopy. Though the vector spaces M+ and M- are not closed under the action of the full Steenrod algebra, the condition that H*(X; * *Z(p)) is torsion free can be combined with the Nishida relations to show that M+ and M- are closed under the action of the subalgebra generated by the reduced power operations. If the integral homology of X is p-torsion free, then the homotopy groups of X are also p-torsion free. hopf.math.purdue.edu /Slack/tfodd.txt   (2262 words)

On the symmetry classes of the first covariant derivatives of tensor fields -- from Mathematica Information Center If σ ∼ [λ] is irreducible then σ[1] has a multiplicity free reduction [λ][1] ∼ ∑ library.wolfram.com /infocenter/Articles/4919   (237 words)

Torsion - Community of Royalty Free Images and Stock Photography Torsion - Community of Royalty Free Images and Stock Photography Register for free and download your first image at NO charge. I have read and agree with the terms and conditions. www.dreamstime.com /retrokidsrecordplayerw/torsion-image27732   (91 words)

Try your search on: Qwika (all wikis)

About us   |   Why use us?   |   Reviews   |   Press   |   Contact us   Copyright © 2005-2007 www.factbites.com Usage implies agreement with terms.