This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS
This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
A comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and continuing through the Giambruno-Zaicev exponential rank. T
This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS
Descartes' philosophy represented one of the most explicit statements of mind-body dualism in the history of philosophy. Its most familiar expression is found in the Meditations (1641) and in Part I of The Principles 0/ Philosophy (1644). However neither of these books provided a detailed discussion of dualism. The Meditations was primarily concerned with finding a foundation for reliable human knowledge, while the Principles attempted to provide an alternative metaphysical framework, in contrast with scholastic philosophy, within which natural philosophy or a scien tific explanation of natural phenomena could be developed. Thus neither book ex plicitly presents a Cartesian theory of the mind nor does either give a detailed account of how, if dualism were accepted, mind and body would interact. The task of articulating such a theory was left to two further works, only one of which was completed by Descartes, viz. the Treatise on Man (published posthumously in 1664). The Treatise began with the following sentence, describing the hypothetical human beings who were to be explained in that work: 'These human beings will be com posed, as we are, of a soul and a body; and, first of all, I must describe the body for you separately; then, also separately, the soul; and fmally I must show you how these two natures would have to be joined and united to constitute human beings resembling us.
Improving education is a key priority for governments around the world. While many suggestions on how best to achieve this are currently under debate, years of academic research have already revealed more about how to encourage change than is sometimes assumed. This volume brings together for the first time some of the most significant work of Karen Seashore Louis, one of the foremost thinkers and researchers in the field. Organizing for School Change presents a unique variety of research-based results from studies conducted over the past twenty-five years. What emerges is not an idealistic plan, but a realistic picture of what needs to be done if schools are to be made better. Drawing on a wide and comprehensive list of sources, the ideas brought together in this collection will prove invaluable and insightful reading, stimulating both newcomers and veterans of the field to consider educational research in new ways.
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