Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

Hypercentral unit groups and the hyperbolicity of a modular group algebra

We classify groups G such that the unit group U-1 (ZG) is hypercentral. In the second part, we classify groups G whose modular group algebra has hyperbolic unit groups U-1 (KG).

Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

Covalent attachment of 3,4,9,10-perylenediimides onto the walls of mesoporous molecular sieves MCM-41 and SBA-15

This work describes the covalent grafting of 3,4,9,10-perylenediimides (PDI), which are fluorescent dyes with very interesting optical properties, onto the walls of mesoporous molecular sieves MCM-41 and SBA-15. The mesoporous materials were first treated with 3-aminopropyltriethoxysilane (APTES) in anhydrous toluene, generating amine-containing surfaces. The amine-containing materials were then reacted with 3,4,9,10-perylenetetracarboxylic dianhydride (PTCA), generating surface-grafted PDI. Infrared spectra of the materials showed that the reaction with amino groups took place at both anhydride ends of the PTCA molecule, resulting in surface attached diimides. No sign of unreacted anhydride groups were found. The new materials, designated as MCMN2PDI and SBAN(2)PDI, presented absorption and emission spectra corresponding to weakly coupled PDI chromophores, in contrast to the strongly coupled rings usually found in solid PDI samples. The materials showed a red fluorescence, which could be observed by the naked eye under UV irradiation or with a fluorescence microscope. The PDI-modified mesoporous materials showed electrical conductivity when pressed into a pellet. The results presented here show that the new materials are potentially useful in the design of nanowires. (C) 2007 Elsevier Inc. All rights reserved.

Negishi cross-coupling of organotellurium compounds: synthesis of biaryls, aryl-, and diaryl acetylenes

A functional group tolerant palladium-catalyzed Negishi coupling of diaryl tellurides with organozinc has been developed. This methodology permits efficient preparation of biaryls, aryl acetylenes and diaryl acetylenes in moderate to good yields. A preliminary study to gain further insight into the reaction was performed using in situ ReactIR technology. (C) 2011 Elsevier Ltd. All rights reserved.

Metabolism of (-)-grandisin from Piper solmsianum in Coleoptera and Lepidoptera species

The biotransformation of the major Piper solmsianum leaf phenylpropanoids, such as the tetrahydrofuran lignan grandisin and derivatives was investigated in the beetle Naupactus bipes as well as in the caterpillars Heraclides hectorides and Quadrus u-lucida. Analysis of fecal material indicated that metabolism occurred mainly through mono- and di-O-demethylation at para positions of 3,4,5-trimethoxyphenyl rings of tetrahydrofuran lignans during digestion by these insects. Additionally, 3-hydroxy-4,5-dimethoxycinnamyl and 3,4,5-trimethoxycinnamyl alcohols were identified in fecal extracts of N. bipes. (C) 2008 Elsevier Ltd. 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.