605 research outputs found
Factorizations of Elements in Noncommutative Rings: A Survey
We survey results on factorizations of non zero-divisors into atoms
(irreducible elements) in noncommutative rings. The point of view in this
survey is motivated by the commutative theory of non-unique factorizations.
Topics covered include unique factorization up to order and similarity, 2-firs,
and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and
Jordan and generalizations thereof. We recall arithmetical invariants for the
study of non-unique factorizations, and give transfer results for arithmetical
invariants in matrix rings, rings of triangular matrices, and classical maximal
orders as well as classical hereditary orders in central simple algebras over
global fields.Comment: 50 pages, comments welcom
Noncommutative generalizations of theorems of Cohen and Kaplansky
This paper investigates situations where a property of a ring can be tested
on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky,
we show that every right ideal of a ring is finitely generated (resp.
principal) iff every "prime right ideal" is finitely generated (resp.
principal), where the phrase "prime right ideal" can be interpreted in one of
many different ways. We also use our methods to show that other properties can
be tested on special sets of right ideals, such as the right artinian property
and various homological properties. Applying these methods, we prove the
following noncommutative generalization of a result of Kaplansky: a (left and
right) noetherian ring is a principal right ideal ring iff all of its maximal
right ideals are principal. A counterexample shows that the left noetherian
hypothesis cannot be dropped. Finally, we compare our results to earlier
generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor
changes were made to the numbering system, in order to remain consistent with
the published versio
Counting and effective rigidity in algebra and geometry
The purpose of this article is to produce effective versions of some rigidity
results in algebra and geometry. On the geometric side, we focus on the
spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic
hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum
determines the commensurability class of the 2-manifold (resp., 3-manifold). We
establish effective versions of these rigidity results by ensuring that, for
two incommensurable arithmetic manifolds of bounded volume, the length sets
(resp., the complex length sets) must disagree for a length that can be
explicitly bounded as a function of volume. We also prove an effective version
of a similar rigidity result established by the second author with Reid on a
surface analog of the length spectrum for hyperbolic 3-manifolds. These
effective results have corresponding algebraic analogs involving maximal
subfields and quaternion subalgebras of quaternion algebras. To prove these
effective rigidity results, we establish results on the asymptotic behavior of
certain algebraic and geometric counting functions which are of independent
interest.Comment: v.2, 39 pages. To appear in Invent. Mat
Search for time-dependent B0s - B0s-bar oscillations using a vertex charge dipole technique
We report a search for B0s - B0s-bar oscillations using a sample of 400,000
hadronic Z0 decays collected by the SLD experiment. The analysis takes
advantage of the electron beam polarization as well as information from the
hemisphere opposite that of the reconstructed B decay to tag the B production
flavor. The excellent resolution provided by the pixel CCD vertex detector is
exploited to cleanly reconstruct both B and cascade D decay vertices, and tag
the B decay flavor from the charge difference between them. We exclude the
following values of the B0s - B0s-bar oscillation frequency: Delta m_s < 4.9
ps-1 and 7.9 < Delta m_s < 10.3 ps-1 at the 95% confidence level.Comment: 18 pages, 3 figures, replaced by version accepted for publication in
Phys.Rev.D; results differ slightly from first versio
Giant breast tumors: Surgical management of phyllodes tumors, potential for reconstructive surgery and a review of literature
<p>Abstract</p> <p>Background</p> <p>Phyllodes tumors are biphasic fibroepithelial neoplasms of the breast. While the surgical management of these relatively uncommon tumors has been addressed in the literature, few reports have commented on the surgical approach to tumors greater than ten centimeters in diameter – the giant phyllodes tumor.</p> <p>Case presentation</p> <p>We report two cases of giant breast tumors and discuss the techniques utilized for pre-operative diagnosis, tumor removal, and breast reconstruction. A review of the literature on the surgical management of phyllodes tumors was performed.</p> <p>Conclusion</p> <p>Management of the giant phyllodes tumor presents the surgeon with unique challenges. The majority of these tumors can be managed by simple mastectomy. Axillary lymph node metastasis is rare, and dissection should be limited to patients with pathologic evidence of tumor in the lymph nodes.</p
Measurement of the branching fraction and CP content for the decay B(0) -> D(*+)D(*-)
This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APS.We report a measurement of the branching fraction of the decay B0→D*+D*- and of the CP-odd component of its final state using the BABAR detector. With data corresponding to an integrated luminosity of 20.4 fb-1 collected at the Υ(4S) resonance during 1999–2000, we have reconstructed 38 candidate signal events in the mode B0→D*+D*- with an estimated background of 6.2±0.5 events. From these events, we determine the branching fraction to be B(B0→D*+D*-)=[8.3±1.6(stat)±1.2(syst)]×10-4. The measured CP-odd fraction of the final state is 0.22±0.18(stat)±0.03(syst).This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A.P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation
Measurement of D-s(+) and D-s(*+) production in B meson decays and from continuum e(+)e(-) annihilation at √s=10.6 GeV
This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APSNew measurements of Ds+ and Ds*+ meson production rates from B decays and from qq̅ continuum events near the Υ(4S) resonance are presented. Using 20.8 fb-1 of data on the Υ(4S) resonance and 2.6 fb-1 off-resonance, we find the inclusive branching fractions B(B⃗Ds+X)=(10.93±0.19±0.58±2.73)% and B(B⃗Ds*+X)=(7.9±0.8±0.7±2.0)%, where the first error is statistical, the second is systematic, and the third is due to the Ds+→φπ+ branching fraction uncertainty. The production cross sections σ(e+e-→Ds+X)×B(Ds+→φπ+)=7.55±0.20±0.34pb and σ(e+e-→Ds*±X)×B(Ds+→φπ+)=5.8±0.7±0.5pb are measured at center-of-mass energies about 40 MeV below the Υ(4S) mass. The branching fractions ΣB(B⃗Ds(*)+D(*))=(5.07±0.14±0.30±1.27)% and ΣB(B⃗Ds*+D(*))=(4.1±0.2±0.4±1.0)% are determined from the Ds(*)+ momentum spectra. The mass difference m(Ds+)-m(D+)=98.4±0.1±0.3MeV/c2 is also measured.This work was supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the Swiss NSF, A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation
A Study of B0 -> J/psi K(*)0 pi+ pi- Decays with the Collider Detector at Fermilab
We report a study of the decays B0 -> J/psi K(*)0 pi+ pi-, which involve the
creation of a u u-bar or d d-bar quark pair in addition to a b-bar -> c-bar(c
s-bar) decay. The data sample consists of 110 1/pb of p p-bar collisions at
sqrt{s} = 1.8 TeV collected by the CDF detector at the Fermilab Tevatron
collider during 1992-1995. We measure the branching ratios to be BR(B0 -> J/psi
K*0 pi+ pi-) = (8.0 +- 2.2 +- 1.5) * 10^{-4} and BR(B0 -> J/psi K0 pi+ pi-) =
(1.1 +- 0.4 +- 0.2) * 10^{-3}. Contributions to these decays are seen from
psi(2S) K(*)0, J/psi K0 rho0, J/psi K*+ pi-, and J/psi K1(1270)
Diffractive Dijet Production at sqrt(s)=630 and 1800 GeV at the Fermilab Tevatron
We report a measurement of the diffractive structure function of
the antiproton obtained from a study of dijet events produced in association
with a leading antiproton in collisions at GeV at the
Fermilab Tevatron. The ratio of at GeV to
obtained from a similar measurement at GeV is compared with
expectations from QCD factorization and with theoretical predictions. We also
report a measurement of the (-Pomeron) and ( of parton in
Pomeron) dependence of at GeV. In the region
, GeV and , is
found to be of the form , which obeys
- factorization.Comment: LaTeX, 9 pages, Submitted to Phys. Rev. Letter
- …