Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.

Health, Justice, and Fairness

In this study I will endeavor to show that the American system of health care violates any conception of distributive justice understood as equality of opportunity. This system fails to provide equal access through a lack of universal insurance, a consumer driven conception of quality, and a system wide focus on cost control, leaving millions of Americans exposed to the ravages of disease. However, if health is understood as an antecedent for one's ability to function across a number of categories that have been objectively deemed as vital to engage in a life that is fully human than the commitment our nation has to the protection of fair equality of opportunity, established by our adoption of a Rawlsian conception of justice, necessitates a revision of our nation's conception of quality to encapsulate health outcomes as well as the advent of a system of universal coverage. Quality care will come to be understood as care that returns to the patient the ability to function across those categories of functioning that illness has jeopardized, and this conception of quality will precipitate system wide reform geared at the creation of positive health outcomes. This paper will articulate this argument by reconstructing and synthesizing precepts from the contemporary philosophical sources and then applying these to the practical workings of our healthcare system, while concurrently demonstrating that a system of distributive justice is compatible with the creation of a universal system of healthcare.