Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

The origin of ring strain and conformational flexibility in Tri- and Tetrasiloxane Rings and their heavier group 14 congeners

Never change a winning team. Since the appearance of the first volume in 1994 this series has become a well respected forum, and like its highly successful predecessors, this sixth volume again brings together leading experts from academia and industry to provide a comprehensive and critical survey of the frontiers of current industrial and university research. - Synthesis and characterization of new organosilicon compounds - Applications in polymer and materials science - Summary of the latest research results The result is a unique compendium with two volumes of first-hand information, vital for all experts working in this field.

A New Fluorinated Polymer Having Two Connected Rings in the Main Chain: Synthesis and Characterization of Fluorinated Poly(1,3-cyclohexadiene)

The high electronegativity and small size of the fluorine atom and the high stability of C-F bonds impart interesting properties and applications to fluorine containing polymers. The unique properties of fluoropolymers include high thermal stability, improved chemical resistance, low surface energies, low coefficients of friction, and low dielectric constants. Applications of fluorinated polymers include use as noncorrosive materials, polymer processing aids, chemically resistant and antifouling coatings, as well as interlayer dielectrics. Fluorine-containing polymers can be directly synthesized via polymerization of fluorine-containing monomers or by post-polymerization modification. The latter method can be used to attach fluorinated species, such as perfluoroalkyl groups, onto conventional polymer chains, thereby imparting properties of fluorine-containing polymers into conventional polymers and widening their range of potential applications.

Twists, knots, and rings in proteins: Structural definition of the cyclotide framework

In recent years an increasing number of miniproteins containing an amide-cyclized backbone have been discovered. The cyclotide family is the largest group of such proteins and is characterized by a circular protein backbone and six conserved cysteine residues linked by disulfide bonds in a tight core of the molecule. These form a cystine knot in which an embedded ring formed by two of the disulfide bonds and the connecting backbone segment is threaded by a third disulfide bond. In the current study we have undertaken high resolution structural analysis of two prototypic cyclotides, kalata B1 and cycloviolacin O1, to define the role of the conserved residues in the sequence. We provide the first comprehensive analysis of the topological features in this unique family of proteins, namely rings (a circular backbone), twists (a cis-peptide bond in the Mobius cyclotides) and knots (a knotted arrangement of the disulfide bonds).

STRUCTURE AND FUNCTION OF THE GROUP III CHAPERONINS, A UNIQUE CLADE OF PROTEIN FOLDING NANOMACHINES

The survival and descent of cells is universally dependent on maintaining their proteins in a properly folded condition. It is widely accepted that the information for the folding of the nascent polypeptide chain into a native protein is encrypted in the amino acid sequence, and the Nobel Laureate Christian Anfinsen was the first to demonstrate that a protein could spontaneously refold after complete unfolding. However, it became clear that the observed folding rates for many proteins were much slower than rates estimated in vivo. This led to the recognition of required protein-protein interactions that promote proper folding. A unique group of proteins, the molecular chaperones, are responsible for maintaining protein homeostasis during normal growth as well as stress conditions. Chaperonins (CPNs) are ubiquitous and essential chaperones. They form ATP-dependent, hollow complexes that encapsulate polypeptides in two back-to-back stacked multisubunit rings, facilitating protein folding through highly cooperative allosteric articulation. CPNs are usually classified into Group I and Group II. Here, I report the characterization of a novel CPN belonging to a third Group, recently discovered in bacteria. Group III CPNs have close phylogenetic association to the Group II CPNs found in Archaea and Eukarya, and may be a relic of the Last Common Ancestor of the CPN family. The gene encoding the Group III CPN from Carboxydothermus hydrogenoformans and Candidatus Desulforudis audaxviator was cloned in E. coli and overexpressed in order to both characterize the protein and to demonstrate its ability to function as an ATPase chaperone. The opening and closing cycle of the Chy chaperonin was examined via site-directed mutations affecting the ATP binding site at R155. To relate the mutational analysis to the structure of the CPN, the crystal structure of both the AMP-PNP (an ATP analogue) and ADP bound forms were obtained in collaboration with Sun-Shin Cha in Seoul, South Korea. The ADP and ATP binding site substitutions resulted in frozen forms of the structures in open and closed conformations. From this, mutants were designed to validate hypotheses regarding key ATP interacting sites as well as important stabilizing interactions, and to observe the physical properties of the resulting complexes by calorimetry.

The impact of unique characteristics of projects and project-based organisations on knowledge transfer

Knowledge has been recognised as an important organisational asset that increases in value when shared; the opposite to other organisational assets which decrease in value during their exploitation. Effective knowledge transfer in organisations helps to achieve and maintain competitive advantage and ultimately organisational success. So far, the research on knowledge transfer has focused on traditional (functional) organisations. Only recently has attention been directed towards knowledge transfer in projects. Existing research on project learning has recognised the need for knowledge transfer within and across projects in project-based organisations (PBOs). Most projects can provide valuable new knowledge from unexpected actions, approaches or problems experienced during the project phases. The aim of this paper is to demonstrate the impact of unique projects characteristics on knowledge transfer in PBO. This is accomplished through review of the literature and a series of interviews with senior project practitioners. The interviews complement the findings from the literature. Knowledge transfer in projects occurs by social communication and transfer of lessons learned where project management offices (PMOs) and project managers play significant roles in enhancing knowledge transfer and communication within the PBO and across projects. They act as connectors between projects and the PBO ‘hub’. Moreover, some project management processes naturally facilitate knowledge transfer across projects. On the other hand, PBOs face communication challenges due to unique and temporary characteristics of projects. The distance between projects and the lack or weakness of formal links across projects, create communication problems that impede knowledge transfer across projects. The main contribution of this paper is to demonstrate that both social communication and explicit informational channels play important role in inter-project knowledge transfer. Interviews also revealed the important role organisational culture play in knowledge transfer in PBOs.

Identifying influences of driving behaviour : could the Australian work driving setting be unique?

Work-related driving safety is an emerging concern for Australian and overseas organisations. An in depth investigation was undertaken into a group of fleet drivers’ attitudes regarding what personal and environment factors have the greatest impact upon driving behaviours. A number of new and unique factors not previously identified were found including: vehicle features, vehicle ownership, road conditions, weather, etc. The major findings of the study are discussed in regards to practical solutions to improve fleet safety.

Knowledge transfer in project-based organisations : the need for a unique approach

Effective knowledge transfer between infrastructure projects plays a significant role in organisational success and discovery of new technologies, helping to achieve and maintain competitive advantage and, in effect, sustainable infrastructure development. Knowledge is recognised as an important organisational asset that adds value while being shared. To date, research on knowledge transfer has focused on traditional (functional) types of organisations. However, existing knowledge transfer approaches fail to address the issue of unique characteristics of project-based organisations, and the fact that functional and project-based organisations significantly differ in terms of structure, processes, and characteristics. Therefore, there is a need for a different, separate approach for managing knowledge in the project environment. The aim of this chapter is to highlight this need. An extensive literature review is provided on the areas of project management, knowledge management, and organisational structure; this is further supported by empirical evidence from interviews with project management practitioners. Conducting a ‘cross-field’ literature review provides a better understanding of the knowledge transfer mechanisms and its application to projects, and of the importance of knowledge transfer across projects. This research is crucial to gaining a better understanding of knowledge transfer in the project environment. It stresses that there are dissimilarities between project-based organisations and functional organisations in terms of organisational structure, duration of processes, viewpoint of time, response to change, and mobility of people, and that there is a need for a unique strategic approach in order to achieve effective transfer of knowledge. Furthermore, findings presented in this chapter reveal key elements that play an important role in across project knowledge transfer. These elements include: social communication, lessons learned databases, and project management offices.

Dealing with unique interests in Crown Land : a Queensland perspective

Security of tenure is the cornerstone of the land management system in Australia. Freehold title is protected throug indefeasibility of title entrenched in legislation and protection of registrable interests in land is offered through the Statutory Assurance Fund. For those with interests pertaining to Crown Land no such protection is offered, although this position is not uniform across Australia. Notably those with Crown leasehold interests or a profit a prendre on Crown Land in Queensland are not protected through registration on the freehold land register and do not have the benefit of indefeasibility of title. The issue of management of interests pertaining to Crown Land has become increasingly relevant due to the complexities associated with balancing public interests including native title with more commercial interests in land generated through carbon sequestration, forestry and mining. This paper considers the framework for the management of Crown Land in Queensland and the adequacy of this framework for commercial interests that pertain to Crown Land.

An investigation of unique challenges in National Historic relics and scenic sites (NHRSSs) in Chinese research literature 1982-2008 using co-word analysis

National Housing Relics and Scenic Sites (NHRSSs) in China are the equivalent of National Parks in the West but have contrasting features and broader roles when compared to their Western counterparts. By reviewing and analysing more than 370 academic sources, this paper identifies 6 major issue clusters and future challenges that will influence the management of NHRSSs over time. It also provides a number of cases to illustrate the particular features of NHRSSs. Identifying the hot issues and important challenges in Chinese NHRSSs will provide valuable insights into priorities now being discussed in highly populated areas of the World.