2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64382In this paper we give a criterion for an ideal of a TAF algebra to be meet irreducible. We show that an ideal $J$ of $A$ is meet irreducile if and only if the C$^*$-envelope of the quotient $A/J$ is primitive. In that case, A/J admits a nest representation which extends to a *-representation of the C$^*$-envelope for $A/J.$ We also characterize the meet irreducible ideals as the kernels of nest representations; this settles the question of whether the n-primitive and meet irreducible ideals coincide.8 pages; accepted in JFAOperator Algebras47D25; 46M40text