HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Z-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

Magnetic-field asymmetry of nonlinear transport in a small ring

We have investigated the magnetic-field asymmetry of the conductance in the nonlinear regime in a small Aharonov-Bohm ring. We have found that the odd-in B and linear in V (the DC bias) correlation function of the differential conductance exhibits periodical oscillations with the Aharonov-Bohm flux. We have deduced the electron interaction constant and analyzed the phase rigidity of the Aharonov-Bohm oscillations in the nonlinear regime. Copyright (C) EPLA, 2009

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

Cwc24p, a novel Saccharomyces cerevisiae nuclear ring finger protein, affects pre-snoRNA U3 splicing

U3 snoRNA is transcribed from two intron-containing genes in yeast, snR17A and snR17B. Although the assembly of the U3 snoRNP has not been precisely determined, at least some of the core box C/D proteins are known to bind pre-U3 co-transcriptionally, thereby affecting splicing and 3 `-end processing of this snoRNA. We identified the interaction between the box C/D assembly factor Nop17p and Cwc24p, a novel yeast RING finger protein that had been previously isolated in a complex with the splicing factor Cef1p. Here we show that, consistent with the protein interaction data, Cwc24p localizes to the cell nucleus, and its depletion leads to the accumulation of both U3 pre-snoRNAs. U3 snoRNA is involved in the early cleavages of 35 S pre-rRNA, and the defective splicing of pre-U3 detected in cells depleted of Cwc24p causes the accumulation of the 35 S precursor rRNA. These results led us to the conclusion that Cwc 24p is involved in pre-U3 snoRNA splicing, indirectly affecting pre-rRNA processing.

A Ring Contraction Strategy toward a Diastereoselective Total Synthesis of (+)-Bakkenolide A

A diastereoselective route to (+)-bakkenolide A is presented from the readily available optically active Wieland-Miescher ketone. This novel synthesis of this sesquiterpene lactone features the following as key stereoselective transformations: (i) the ring contraction reaction of a octalone mediated by thallium(III) nitrate (TTN); (ii) a hydrogenation to create the cis-fused junction; and (iii) the formation of the C7 quaternary center through an enolate intermediate. Furthermore, during this work, the absolute configuration of a trinorsesquiterpene isolated from Senecio Humillimus was assigned.

The soft nucleophilicity of organotellurolates driving the S(N)2-type lactone ring-opening reaction

Lithium and magnesium organotellurolates were reacted with lactones producing the corresponding tellurocarboxylic acids. Treatment of the reaction mixture with lithium aluminum hydride allowed the isolation of the corresponding hydroxytellurides in a one-pot operation. (C) 2009 Published by Elsevier Ltd

Practical synthesis of chiral beta-telluro amines by ring-opening reaction of aziridines

A set of chiral beta-tellurium amines and their selenium and sulfur-containing derivatives have been efficiently synthesized in good to excellent yields via the ring-opening reaction of chiral aziridines by chalcogen nucleophilic species. (C) 2008 Elsevier B.V. All rights reserved.

Iodine(III)-promoted ring expansion of 1-vinylcycloalkanol derivatives: A metal-free approach toward seven-membered rings

A versatile and metal-free approach for the synthesis of molecules bearing seven- and eight-membered rings is described. The strategy is based on the ring expansion of 1-vinylcycloalkanols (or the corresponding silyl or methyl ether) mediated by the hypervalent iodine reagent HTIB (Phl(OH)OTs). The reaction condition can be easily adjusted to give seven-membered rings bearing different functional groups. A route to medium-ring lactones was also developed.

Ring Contraction of 1,2-Dihydronaphthalenes Promoted by Thallium(III) in Acetonitrile: A Diastereoselective Approach to Indanes

trans-1,3-Disubstituted indanes are conveniently accessed by a stereoselective ring contraction of 1,2-dihydronaphthalenes upon treatment with thallium(III) nitrate (TTN) in acetonitrile. Under these conditions, the oxidative rearrangement of either di- or trisubstituted double bonds is possible.

A Diastereoselective Total Synthesis of trans-Trikentrin A: A Ring Contraction Approach

A new route to obtain the polyalkylated indole (+/-)-trans-trikentrin A was developed. The synthesis of this natural alkaloid features a thallium(III)mediated ring contraction reaction to obtain the trans-1,3-disubstituted five-membered ring in a diastereoselective manner. Thallium(III) is chemoselective in this rearrangement, reacting with the olefin without oxidation of the indole moiety. Other key transformations are the Bartoli`s reaction to construct the heterocyclic ring and a Heck coupling to add the carbons atom that will originate the nonaromatic cycle.