This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization str
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to ma
This two-volume course on abstract algebra provides a broad introduction to the subject for those with no previous knowledge of it but who are well grounded in ordinary algebraic techniques. It starts from the beginning, leading up to fresh ideas gradually and in a fairly elementary manner, and moving from discussion of particular (concrete) cases to abstract ideas and methods. It thus avoids the common practice of presenting the reader with a mass of ideas at the beginning, which he is only later able to relate to his previous mathematical experience. The work contains many concrete examples of algebraic structures. Each chapter contains a few worked examples for the student - these are divided into straightforward and more advanced categories. Answers are provided. From general sets, Volume 1 leads on to discuss special sets of the integers, other number sets, residues, polynomials and vectors. A chapter on mappings is followed by a detailed study of the fundamental laws of algebra,
Among the topics explored in this book are ways of viewing the soul, the relation between body and soul, environmentalist thought, the phenomenon of torture, and the philosophical and theological warrants for genocide. Presenting an analysis of abstract modes of thought that have contributed to genocide, the book argues that a Jewish model of concrete thinking may inform our understanding of the abstractions that can lead to genocide. Its aim is to draw upon distinctively Jewish categories of thought to demonstrate how the conceptual defacing of the other human being serves to promote the murder of peoples, and to suggest a way of thinking that might help prevent genocide.
Among the topics explored in this book are ways of viewing the soul, the relation between body and soul, environmentalist thought, the phenomenon of torture, and the philosophical and theological warrants for genocide. Presenting an analysis of abstract modes of thought that have contributed to genocide, the book argues that a Jewish model of concrete thinking may inform our understanding of the abstractions that can lead to genocide. Its aim is to draw upon distinctively Jewish categories of thought to demonstrate how the conceptual defacing of the other human being serves to promote the murder of peoples, and to suggest a way of thinking that might help prevent genocide.
