On Vinberg ( − 1,1) rings

2016 ◽  
Vol 09 (04) ◽  
pp. 1650070 ◽  
Author(s):  
K. Jayalakshmi ◽  
G. Lakshmi Devi
Keyword(s):  
Root Space ◽  
One Dimensional ◽  
Lie Ring ◽  
Solvable Radical ◽  
Nonzero Root ◽  
Levi Factor ◽  
Torsion Free

We give a description of a 2-torsion free Vinberg ([Formula: see text]) ring [Formula: see text]. If every nonzero root space of [Formula: see text] for [Formula: see text] is one-dimensional where [Formula: see text] is a split abelian Cartan subring of [Formula: see text] which is nil on [Formula: see text] then [Formula: see text] is a Lie ring isomorphic to [Formula: see text]. This generalizes the known result obtained by Myung for the case that [Formula: see text] is a 2-torsion free Vinberg ([Formula: see text]) ring and is power associative. We also give a condition that a Levi factor [Formula: see text] of [Formula: see text] be an ideal of [Formula: see text] when the solvable radical of [Formula: see text] is nilpotent. We apply these results for reductive case of [Formula: see text].

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

Rings with simple Lie rings of Lie and Jordan derivations

2018 ◽  
Vol 17 (04) ◽  
pp. 1850078
Author(s):  
Ahmad Al Khalaf ◽  
Orest D. Artemovych ◽  
Iman Taha
Keyword(s):  
Noetherian Ring ◽  
Associative Ring ◽  
Lie Ring ◽  
Lie Rings ◽  
Lie Derivations ◽  
Torsion Free

Let [Formula: see text] be an associative ring. We characterize rings [Formula: see text] with simple Lie ring [Formula: see text] of all Lie derivations, reduced noncommutative Noetherian ring [Formula: see text] with the simple Lie ring [Formula: see text] of all derivations and obtain some properties of [Formula: see text]-torsion-free rings [Formula: see text] with the simple Lie ring [Formula: see text] of all Jordan derivations.

scholarly journals On the Ideal Case of a Conjecture of Huneke and Wiegand

2019 ◽  
Vol 62 (3) ◽  
pp. 847-859 ◽  
Author(s):  
Olgur Celikbas ◽  
Shiro Goto ◽  
Ryo Takahashi ◽  
Naoki Taniguchi
Keyword(s):  
Free Module ◽  
Affirmative Answer ◽  
Noetherian Rings ◽  
Ideal Case ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Integrally Closed ◽  
Integrally Closed Ideals ◽  
Torsion Free ◽  
The Ideal

AbstractA conjecture of Huneke and Wiegand claims that, over one-dimensional commutative Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free module with its algebraic dual always has torsion. Building on a beautiful result of Corso, Huneke, Katz and Vasconcelos, we prove that the conjecture is affirmative for a large class of ideals over arbitrary one-dimensional local domains. Furthermore, we study a higher-dimensional analogue of the conjecture for integrally closed ideals over Noetherian rings that are not necessarily local. We also consider a related question on the conjecture and give an affirmative answer for first syzygies of maximal Cohen–Macaulay modules.

scholarly journals The Ado theorem for finite Lie conformal algebras with Levi decomposition

2016 ◽  
Vol 15 (07) ◽  
pp. 1650130 ◽  
Author(s):  
Pavel Kolesnikov
Keyword(s):  
Lie Algebra ◽  
Solvable Radical ◽  
Conformal Representation ◽  
Levi Decomposition ◽  
Conformal Algebras ◽  
Torsion Free

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.

FREE GROUPS OF OUTER COMMUTATOR VARIETIES OF GROUPS

2001 ◽  
Vol 64 (2) ◽  
pp. 423-435
Author(s):  
DANIEL P. GROVES
Keyword(s):  
Free Group ◽  
Free Groups ◽  
Lie Ring ◽  
Lie Rings ◽  
Outer Commutator ◽  
Torsion Free ◽  
Group 1

If F is a free group, 1 < i [les ] j [les ] 2i and i [les ] k [les ] i + j + 1 then F/[γj(F), γi(F), γk(F)] is residually nilpotent and torsion-free. This result is extended to 1 < i [les ] j [les ] 2i and i [les ] k [les ] 2i + 2j. It is proved that the analogous Lie rings, L/[Lj, Li, Lk] where L is a free Lie ring, are torsion-free. Candidates are found for torsion in L/[Lj, Li, Lk] whenever k is the least of {i, j, k}, and the existence of torsion in L/[Lj, Li, Lk] is proved when i, j, k [les ] 5 and k is the least of {i, j, k}.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

1990 ◽  
Vol 48 (4) ◽  
pp. 76-77
Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye
Keyword(s):  
Twin Structure ◽  
Modulated Structure ◽  
High Tc ◽  
One Dimensional ◽  
Lattice Constants ◽  
Superconducting Phases ◽  
Modulated Structures ◽  
Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

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