2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78504A nest representation of a strongly maximal TAF algebra $A$ is a representation $π$ for which $\operatorname{Lat} π(A) is totally ordered. We prove that if the spectrum of $A$ is totally ordered, or if $\operatorname{Lat} π(A)$ contains an atom, then $\operatorname{ker} π$ is a meet irreducible ideal.AMS-LaTeX, 17 pages. Revised version corrects a misstatement in the expository material of the main theorem in section 3. Other minor misprints are also corrrectedOperator Algebras47D25text