2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72725In this note, we study the notion of purely infinite simple ring in the case of non-unital rings, and we obtain an analog to Zhang's Dichotomy for $σ$-unital purely infinite simple C*-algebras in the purely algebraic context.Revised version. This paper was accepted for publication in Communications in AlgebraRings and Algebras16D70text