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.

The maximal C*-algebra of quotients as an operator bimodule

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product of A with itself labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.

On the universal TRO of a JC*-triple, ideals and tensor products

In a development from material introduced in recent work, we discuss the interconnections between ternary rings of operators (TROs) and right C*-algebras generated by JC*-triples, deducing that every JC*-triple possesses a largest universally reversible ideal, that the universal TRO commutes with appropriate tensor products and establishing a reversibility criterion for type I JW*-triples.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

UNIFORM APPROXIMATION ON IDEALS OF MULTILINEAR MAPPINGS

For each ideal of multilinear mappings M we explicitly construct a corresponding ideal (a)M such that multilinear forms in (a)M are exactly those which can be approximated, in the uniform norm, by multilinear forms in M. This construction is then applied to finite type, compact, weakly compact and absolutely summing multilinear mappings. It is also proved that the correspondence M bar right arrow (a)M. IS Aron-Berner stability preserving.

Medical treatment and the good death: an ethical analysis of euthanasia, physician assisted suicide, and the right to die

Frequent advances in medical technologies have brought fonh many innovative treatments that allow medical teams to treal many patients with grave illness and serious trauma who would have died only a few years earlier. These changes have given some patients a second chance at life, but for others. these new treatments have merely prolonged their dying. Instead of dying relatively painlessly, these unfortunate patients often suffer from painful tenninal illnesses or exist in a comatose state that robs them of their dignity, since they cannot survive without advanced and often dehumanizing forms of treatment. Due to many of these concerns, euthanasia has become a central issue in medical ethics. Additionally, the debate is impacted by those who believe that patients have the right make choices about the method and timing of their deaths. Euthanasia is defined as a deliberate act by a physician to hasten the death of a patient, whether through active methods such as an injection of morphine, or through the withdrawal of advanced forms of medical care, for reasons of mercy because of a medical condition that they have. This study explores the question of whether euthanasia is an ethical practice and, as determined by ethical theories and professional codes of ethics, whether the physician is allowed to provide the means to give the patient a path to a "good death," rather than one filled with physical and mental suffering. The paper also asks if there is a relevant moral difference between the active and passive forms of euthanasia and seeks to define requirements to ensure fully voluntary decision making through an evaluation of the factors necessary to produce fully informed consent. Additionally, the proper treatments for patients who suffer from painful terminal illnesses, those who exist in persistent vegetative states and infants born with many diverse medical problems are examined. The ultimate conclusions that are reached in the paper are that euthanasia is an ethical practice in certain specific circumstances for patients who have a very low quality of life due to pain, illness or serious mental deficits as a result of irreversible coma, persistent vegetative state or end-stage clinical dementia. This is defended by the fact that the rights of the patient to determine his or her own fate and to autonomously decide the way that he or she dies are paramount to all other factors in decisions of life and death. There are also circumstances where decisions can be made by health care teams in conjunction with the family to hasten the deaths of incompetent patients when continued existence is clearly not in their best interest, as is the case of infants who are born with serious physical anomalies, who are either 'born dying' or have no prospect for a life that is of a reasonable quality. I have rejected the distinction between active and passive methods of euthanasia and have instead chosen to focus on the intentions of the treating physician and the voluntary nature of the patient's request. When applied in equivalent circumstances, active and passive methods of euthanasia produce the same effects, and if the choice to hasten the death of the patient is ethical, then the use of either method can be accepted. The use of active methods of euthanasia and active forms of withdrawal of life support, such as the removal of a respirator are both conscious decisions to end the life of the patient and both bring death within a short period of time. It is false to maintain a distinction that believes that one is active killing. whereas the other form only allows nature to take it's course. Both are conscious choices to hasten the patient's death and should be evaluated as such. Additionally, through an examination of the Hippocratic Oath, and statements made by the American Medical Association and the American College of physicians, it can be shown that the ideals that the medical profession maintains and the respect for the interests of the patient that it holds allows the physician to give aid to patients who wish to choose death as an alternative to continued suffering. The physician is also allowed to and in some circumstances, is morally required, to help dying patients whether through active or passive forms of euthanasia or through assisted suicide. Euthanasia is a difficult topic to think about, but in the end, we should support the choice that respects the patient's autonomous choice or clear best interest and the respect that we have for their dignity and personal worth.

No right to sext? A critical examination of media and legal debates about teenage girls' sexual agency in the digital age

Advances in digital photography and distribution technologies enable many people to produce and distribute images of their sex acts. When teenagers do this, the photos and videos they create can be legally classified as child pornography since the law makes no exception for youth who create sexually explicit images of themselves. The dominant discussions about teenage girls producing sexually explicit media (including sexting) are profoundly unproductive: (1) they blame teenage girls for creating private images that another person later maliciously distributed and (2) they fail to respect—or even discuss—teenagers’ rights to freedom of expression. Cell phones and the internet make producing and distributing images extremely easy, which provide widely accessible venues for both consensual sexual expression between partners and for sexual harassment. Dominant understandings view sexting as a troubling teenage trend created through the combination of camera phones and adolescent hormones and impulsivity, but this view often conflates consensual sexting between partners with the malicious distribution of a person’s private image as essentially equivalent behaviors. In this project, I ask: What is the role of assumptions about teen girls’ sexual agency in these problematic understandings of sexting that blame victims and deny teenagers’ rights? In contrast to the popular media panic about online predators and the familiar accusation that youth are wasting their leisure time by using digital media, some people champion the internet as a democratic space that offers young people the opportunity to explore identities and develop social and communication skills. Yet, when teen girls’ sexuality enters this conversation, all this debate and discussion narrows to a problematic consensus. The optimists about adolescents and technology fall silent, and the argument that media production is inherently empowering for girls does not seem to apply to a girl who produces a sexually explicit image of herself. Instead, feminist, popular, and legal commentaries assert that she is necessarily a victim: of a “sexualized” mass media, pressure from her male peers, digital technology, her brain structures or hormones, or her own low self-esteem and misplaced desire for attention. Why and how are teenage girls’ sexual choices produced as evidence of their failure or success in achieving Western liberal ideals of self-esteem, resistance, and agency? Since mass media and policy reactions to sexting have so far been overwhelmingly sexist and counter-productive, it is crucial to interrogate the concepts and assumptions that characterize mainstream understandings of sexting. I argue that the common sense that is co-produced by law and mass media underlies the problematic legal and policy responses to sexting. Analyzing a range of nonfiction texts including newspaper articles, talk shows, press releases, public service announcements, websites, legislative debates, and legal documents, I investigate gendered, racialized, age-based, and technologically determinist common sense assumptions about teenage girls’ sexual agency. I examine the consensus and continuities that exist between news, nonfiction mass media, policy, institutions, and law, and describe the limits of their debates. I find that this early 21st century post-feminist girl-power moment not only demands that girls live up to gendered sexual ideals but also insists that actively choosing to follow these norms is the only way to exercise sexual agency. This is the first study to date examining the relationship of conventional wisdom about digital media and teenage girls’ sexuality to both policy and mass media.

Ideals, Aesthetics, and Practices of Professionalization in the Tokyo Jazz Scene

In the early twenty-first century, jazz has a history in Japan of approximately 100 years. In contemporary Tokyo, Japanese musicians demonstrate their right to access jazz performance through a variety of musical and extra-musical techniques. Those accepted as fully professional and authentic artists, or puro, gain a special status among their peers, setting them apart from their amateur and part-time counterparts. Drawing on three months of participant-observation in the Tokyo jazz scene, I examine this status of puro, its variable definition, the techniques used by musicians to establish themselves as credible jazz performers, and some obstacles to achieving this status. I claim two things: first, aspiring puro musicians establish themselves within a jazz tradition through musical references to African American identity and a rhetoric of jazz as universal music. Second, I claim that universalism as a core aesthetic creates additional obstacles to puro status for certain musicians in the Tokyo scene.

Applying integrated resource and environmental management to transmission right-of-way maintenance

The concept of a substantive integrator is introduced as a method for integrated resource and environmental management as a means to assimilate different resource values at the operational or field level. A substantive integrator is a strategic management tool for integrating multiple uses into coprorate management regimes that traditionally manage for single values. Wildlife habitat management is presented as a substantive integrator for managing vegetation on electric utility power line corridors. A case study from northern British Columbia provides an example of wildlife habitat management as a means to integrate other resource values such as aesthetics, access and subsistence along British Columbia Hydro and Power Authority's transmission rights-of-way.

HVAC system size – getting it right

There is evidence that many heating, ventilating & air conditioning (HVAC) systems, installed in larger buildings, have more capacity than is ever required to keep the occupants comfortable. This paper explores the reasons why this can occur, by examining a typical brief/design/documentation process. Over-sized HVAC systems cost more to install and operate and may not be able to control thermal comfort as well as a “right-sized” system. These impacts are evaluated, where data exists. Finally, some suggestions are developed to minimise both the extent of, and the negative impacts of, HVAC system over-sizing, for example: • Challenge “rules of thumb” and/or brief requirements which may be out of date. • Conduct an accurate load estimate, using AIRAH design data, specific to project location, and then resist the temptation to apply “safety factors • Use a load estimation program that accounts for thermal storage and diversification of peak loads for each zone and air handling system. • Select chiller sizes and staged or variable speed pumps and fans to ensure good part load performance. • Allow for unknown future tenancies by designing flexibility into the system, not by over-sizing. For example, generous sizing of distribution pipework and ductwork will allow available capacity to be redistributed. • Provide an auxiliary tenant condenser water loop to handle high load areas. • Consider using an Integrated Design Process, build an integrated load and energy use simulation model and test different operational scenarios • Use comprehensive Life Cycle Cost analysis for selection of the most optimal design solutions. This paper is an interim report on the findings of CRC-CI project 2002-051-B, Right-Sizing HVAC Systems, which is due for completion in January 2006.