This is a reissue of a classic text, which includes the author's own corrections and provides a very accessible, self contained introduction to the classical theory of orders and maximal orders over a Dedekind ring. It starts with a long chapter that provides the algebraic prerequisites for this theory, covering basic material on Dedekind domains, localizations and completions, as well as semisimple rings and separable algebras. This is followed by an introduction to the basic tools in studying orders, such as reduced norms and traces, discriminants, and localization of orders. The theory of maximal orders is then developed in the local case, first in a complete setting, and then over any discrete valuation ring. This paves the way to a chapter on the ideal theory in global maximal orders, with detailed expositions on ideal classes, the Jordan-Zassenhaus Theorem, and genera. This is followed by a chapter on Brauer groups and crossed product algebras, where Hasse's theory of cyclic algebras over local fields is presented in a clear and self-contained fashion. Assuming a couple of facts from class field theory, the book goes on to present the theory of simple algebras over global fields, covering in particular Eichler's Theorem on the ideal classes in a maximal order, as well as various results on the KO group and Picard group of orders. The rest of the book is devoted to a discussion of non-maximal orders, with particular emphasis on hereditary orders and group rings. The ideas collected in this book have found important applications in the smooth representation theory of reductive p-adic groups. This text provides a useful introduction to this wide range of topics. It is written at a level suitable for beginning postgraduate students, is highly suited to class teaching and provides a wealth of exercises.
Emotions have emerged as a topic of interest across the disciplines, yet studies and findings on emotions tend to fall into two camps: body versus brain, nature versus nurture. Emotions as Bio-cultural Processes offers a unique collaboration across the biological/social divide—from psychology and neuroscience to cultural anthropology and sociology—as 15 noted researchers develop a common language, theoretical basis, and methodology for examining this most sociocognitive aspect of our lives. Starting with our evolutionary past and continuing into our modern world of social classes and norms, these multidisciplinary perspectives reveal the complex interplay of biological, social, cultural, and personal factors at work in emotions, with particular emphasis on the nuances involved in pride and shame. A sampling of the topics: (1) The roles of the brain in emotional processing. (2) Emotional development milestones in childhood. (3) Social feeling rules and the experience of loss. (4) Emotions as commodities? The management of feelings and the self-help industry. (5) Honor and dishonor: societal and gender manifestations of pride and shame. (6) Emotion regulation and youth culture. (7) Pride and shame in the classroom. A volume of such wide and integrative scope as Emotions as Bio-cultural Processes should attract a large cohort of readers on both sides of the debate, among them emotion researchers, social and developmental psychologists, sociologists, social anthropologists, and others who analyze the links between humans that on the one hand differentiate us as individuals but on the other hand tie us to our socio-cultural worlds.
The aim of the lectures is to provide an introduction to recent developments in the theory of class groups and Picard groups. The techniques employed come from the three main areas: algebraic number theory, representation theory of algebras and orders, and algebraic $K$-theory.
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“Irving looks cunningly beyond the eye-catching gyrations of the mating dance to the morning-after implications.”—The Washington Post The darker vision and sexual ambiguities of this sensual, ironic tale about a ménage a quatre in a New England university town foreshadow those of The World According to Garp; but this very trim and precise novel is a marked departure from the author's generally robust, boisterous style. Though Mr. Irving's cool eye spares none of his foursome, he writes with genuine compassion for the sexual tests and illusions they perpetrate on each other; but the sexual intrigue between them demonstrates how even the kind can be ungenerous, and even the well-intentioned, destructive. “One of the most remarkable things about John Irving's first three novels, viewed from the vantage of The World According to Garp, is that they can be read as one extended fictional enterprise. . . . The 158-Pound Marriage is as lean and concentrated as a mine shaft.”—Terrence Des Pres “Deft, hard-hitting . . . What Irving demonstrates beautifully is that a one-to-one relationship is more demanding than a free-for-all.”—The New York Times Book Review
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