%0 Journal Article %A González-Barroso, M.A. %A Pardo Espino, Enrique %T Structure of non-unital purely infinite simple rings %D 2006 %@ 0092-7872 %U http://hdl.handle.net/10498/16080 %X In this note, we study the notion of purely infinite simple ring in the case of nonunital rings, and we obtain an analog to Zhang's Dichotomy for σ-unital purely infinite simple C*-algebras in the purely algebraic context. %~ Universidad de Cádiz