Topics In Ring Theory

The notes compilied in this book is from a course taught at the University of Chicago in the Spring Qurater of 1964. They were originally published in 1965 in the Lecture Notes of the Mathematics Department of the University of Chicago under the title of "Topics in Ring Theory." this present version is a reworking of these notes -- many of the proofs in the first chapters have been changed and some material has been added. Lie and Jordan Structures in simple rings. Theorems of Goldie and some of their consequences for rings conditioned by some appropriate chain condition. Golod-Shafarevitch theorem and examples due to Bergman and Sasiada. Carus Monograph "Non-Commutative Rings" consists of one of the proofs of Goldie's theorem, ultra-products and Posner's theorem and the Golod-Shafarevitch theorem. Simple rings with Involution; The subring gennerated b y the skew elements; A theorem of Baxter; Jordan simplicity of the symmetric elements; Lie structures of K, the skew elements. Jordan Homomorphisms and Derivations onto prime rings...