A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nestprimitive ideals are also described.

In [4], nests were classified up to similarity simply in terms of order type and dimension. However the proof given there and exposited in [6] appears to rely on first classifying the compact perturbations of the nest algebras. This, in turn, required reliance on some difficult results on derivations of C*-algebras and in particular on the theorem of Johnson and Parrott [7]. However a careful e...