E-Rings and Related Structures

Abstract

Let R be a ring. For s\in R, define s\sb l\colon R\to R bys\sb l(x)=sx for all x\in R. Then R\sb l={s\sb l\colon\s\in R} is a set of \Bbb Z linear maps on R, and R iscalled an E ring if R\sb l={\rm Hom}\sb {\Bbb Z}(R,R). An Rmodule M is called an E module if{\rm Hom}\sb {\Bbb Z}(R,M)={\rm Hom}\sb R(R,M). This article isan excellent survey of the classical results on E rings and Emodules as well as more recent generalizations. Suggestions forfurther research and a list of instances where E ring likestructures show up are also included in this survey.\par {Forthe entire collection see MR 2002c:13002.}