Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

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.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

Partial projective representations and partial actions

The concept of a partial projective representation of a group is introduced and studied. The interaction with partial actions is explored. It is shown that the factor sets of partial projective representations over a field K are exactly the K-valued twistings of crossed products by partial actions. (C) 2009 Elsevier B.V. All rights reserved.

Partial projective representations and partial actions II

This paper is a continuation of Dokuchaev and Novikov (2010) [8]. The interaction between partial projective representations and twisted partial actions of groups considered in Dokuchaev and Novikov (2010) [8] is treated now in a categorical language. In the case of a finite group G, a structural result on the domains of factor sets of partial projective representations of G is obtained in terms of elementary partial actions. For arbitrary G we study the component pM'(G) of totally-defined factor sets in the partial Schur multiplier pM(G) using the structure of Exel's semigroup. A complete characterization of the elements of pM'(G) is obtained for algebraically closed fields. (C) 2011 Elsevier B.V. All rights reserved.

Group Rings – A Brief History and some their Generalizations

We give a brief exposition of the history of the group rings and some their generalizations. Also we indicate some information of certain problems and results.

Trade agreement between the United States and the Czechoslovak republic. Digests of trade data respecting the products on which concessions in tariff treatment were granted by the United States together with a summary of the concessions granted by both countries ...

Lithographed.

The effect of consumer risk perceptions and information search on willingness to buy GM food products: A cross cultural analysis

This paper seeks to address the widespread call in the literature for the cross-cultural examination ( and validation) of accepted concepts within consumer behaviour, such as consumer risk perceptions and information search. The findings of the study provide support for a number of accepted relationships, whilst identifying distinct cross cultural differences in external information search and willingness to buy genetically modified (GM) food products by consumers.

Cooperation using a robotic ad hoc network made from Bluetooth, JXTA, OSGi and other commercial off the shelf (COTS) products

Abstract - Mobile devices in the near future will need to collaborate to fulfill their function. Collaboration will be done by communication. We use a real world example of robotic soccer to come up with the necessary structures required for robotic communication. A review of related work is done and it is found no examples come close to providing a RANET. The robotic ad hoc network (RANET) we suggest uses existing structures pulled from the areas of wireless networks, peer to peer and software life-cycle management. Gaps are found in the existing structures so we describe how to extend some structures to satisfy the design. The RANET design supports robot cooperation by exchanging messages, discovering needed skills that other robots on the network may possess and the transfer of these skills. The network is built on top of a Bluetooth wireless network and uses JXTA to communicate and transfer skills. OSGi bundles form the skills that can be transferred. To test the nal design a reference implementation is done. Deficiencies in some third party software is found, specifically JXTA and JamVM and GNU Classpath. Lastly we look at how to fix the deciencies by porting the JXTA C implementation to the target robotic platform and potentially eliminating the TCP/IP layer, using UDP instead of TCP or using an adaptive TCP/IP stack. We also propose a future areas of investigation; how to seed the configuration for the Personal area network (PAN) Bluetooth protocol extension so a Bluetooth TCP/IP link is more quickly formed and using the STP to allow multi-hop messaging and transfer of skills.

The S.T.A.B. Trial - Standardised Testing of Artificial Blood. A comparative study of various products that may be used as artificial blood for high fidelity simulation training in the critical care setting

Aim: In the current climate of medical education, there is an ever-increasing demand for and emphasis on simulation as both a teaching and training tool. The objective of our study was to compare the realism and practicality of a number of artificial blood products that could be used for high-fidelity simulation. Method: A literature and internet search was performed and 15 artificial blood products were identified from a variety of sources. One product was excluded due to its potential toxicity risks. Five observers, blinded to the products, performed two assessments on each product using an evaluation tool with 14 predefined criteria including color, consistency, clotting, and staining potential to manikin skin and clothing. Each criterion was rated using a five-point Likert scale. The products were left for 24 hours, both refrigerated and at room temperature, and then reassessed. Statistical analysis was performed to identify the most suitable products, and both inter- and intra-rater variability were examined. Results: Three products scored consistently well with all five assessors, with one product in particular scoring well in almost every criterion. This highest-rated product had a mean rating of 3.6 of 5.0 (95% posterior Interval 3.4-3.7). Inter-rater variability was minor with average ratings varying from 3.0 to 3.4 between the highest and lowest scorer. Intrarater variability was negligible with good agreement between first and second rating as per weighted kappa scores (K = 0.67). Conclusion: The most realistic and practical form of artificial blood identified was a commercial product called KD151 Flowing Blood Syrup. It was found to be not only realistic in appearance but practical in terms of storage and stain removal.