| Given any associative ring R we can render it into a Lie ring by defining, for any two elements a,b R, a new product, the Lie product, defined by〔a,b〕= ab-ba. Similarly we can make of it a Jordan ring by introducing the Jordan product a。b = ab+ba. It is natural to expect that the associative properties of the ring R should reflect heavily in the properties of R as a Lie and a Jordan ring. The influence on these of the assumption that R is a simple ring will be our concern. |