2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152414We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural extension of one description of meet irreducible ideals in the upper triangular matrices. Additional information is available if the limit algebra is an analytic subalgebra of its C*-envelope or if the analytic algebra is trivially analytic with an injective 0-cocycle. Completely meet irreducible ideals are considered, and a distance formula is presented.AMS-TeX v2.1, 27 pages with no figuresFunctional AnalysisOperator Algebras46K50 (Primary) 46H10 (Secondary)text