Representations of Rings over Skew Fields

by A. H. Schofield

Overview

The first half of the book is a general study of homomorphisms to simple artinian rings; the techniques developed here should be of interest to many algebraists. The second half is a more detailed study of special types of skew fields which have arisen from the work of P. M. Cohn and the author. A number of questions are settled; a version of the Jacobian conjecture for free algebras is proved and there are examples of skew field extensions of different but finite left and right dimension.

Product Details

ISBN-13:	9780521278539
Publisher:	Cambridge University Press
Publication date:	04/18/1985
Series:	London Mathematical Society Lecture Note Series , #92
Pages:	236
Product dimensions:	5.98(w) x 8.98(h) x 0.87(d)

Table of Contents

Part I. Homomorphisms to simple artinian rings: 1. Hereditary rings and projective rank functions; 2. The coproduct theorems; 3. Projective rank functions on ring coproducts; 4. Universal localisation; 5. Universal homomorphisms from hereditary to simple artinian rings; 6. Homomorphisms from hereditary to von Neumann regular rings; 7. Homomorphisms from rings to simple artinian rings; Part II. Skew subfields of simple artinian coproducts: 8. The centre of the simple artinian coproduct; 9. Finite dimensional divisions subalgebras of skew field coproducts; 10. The universal bimodule of derivations; 11. Commutative subfields and centralisers in skew held coproducts; 12. Characterising universal localisations at a rank function; 13. Bimodule amalgam rings and Artin's problem; References; Index.