Representations of Rings over Skew Fields [Paperback]

A study of representations of rings over skew fields.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.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.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.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.