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Finite-Dimensional Division Algebras over Fields

  • Authors
  • Nathan┬áJacobson

Table of contents

  1. Front Matter
    Pages i-viii
  2. Nathan Jacobson
    Pages 1-40
  3. Nathan Jacobson
    Pages 41-94
  4. Nathan Jacobson
    Pages 95-153
  5. Nathan Jacobson
    Pages 154-184
  6. Nathan Jacobson
    Pages 185-274
  7. Back Matter
    Pages 275-283

About this book

Introduction

Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm.

Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).

Keywords

Associative Rings Commutative Rings Nonassociative Ring Theory algebra associative ring commutative ring field matrices polynomial ring ring theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-02429-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57029-5
  • Online ISBN 978-3-642-02429-0
  • Buy this book on publisher's site