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. 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.