Ske Fields [Paperback]

This book will be of interest to graduate students in pure mathematics and to professional mathematicians.The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals.The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals.The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals. The principal topic discussed in this section is reduced K,-theory. This book will be of interest to graduate students in pure mathematics and to professional mathematicians.Preface; Conventions on terminology; Part I. Skew Fields and Simple Rings: 1. Some ad hoc results on skew fields; 2. Rings of matrices over skew fields; 3. Simple rings and Wedderburn's main theorem; 4. A short cut to tensor products; 5. Tensor products and algebras; 6. Tensor products and Galois theory; 7. Skolem-Noether theorem and Centralizer theorem; 8. The corestriction of algebras; Part II. Skew Fields and Brauer Groups: 9. Brauer groups over fields; 10. Cyclic algebras; 11. Power norm residue algebras; 12. Brauer groups and Galois cohomology; 13. The formalism ol��