2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153596The radical $J(V)$ of a vertex operator algebra $V$ is defined to be the subspace of $V$ consisting of vectors $v$ such that the zero mode $o(v)=0$ on $V$ where $o(v)=v_{wt v-1}$ if $v$ is homogeneous. We establish various facts about $o(v),$ including the determination of $J(V)$ which is shown to be essentially equal to $(L(0)+L(-1))V.$tex 10 pages, to appear in : Proc. of the Conference on the Monster and Lie algebras at The Ohio State University, May 1996Quantum Algebratext