Representations of Rings over Skew Fields
Representations of Rings over Skew Fields
A. H. Schofield
April 1985
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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.
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9780511892035
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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.
