A nest representation of a strongly maximal TAF algebra
A
is a representation
π
for which
Latπ(A)istotallyordered.Weprovethatifthespectrumof
A
istotallyordered,orif
\operatorname{Lat} \pi(A)
containsanatom,then
\operatorname{ker} \pi$ is a meet irreducible ideal.