  A notion of partial ideal for an operator algebra is a weakening the notion
of ideal where the defining algebraic conditions are enforced only in the
commutative subalgebras. We show that, in a von Neumann algebra, the
ultraweakly closed two-sided ideals, which we call total ideals, correspond to
the unitarily invariant partial ideals. The result also admits an equivalent
formulation in terms of central projections. We place this result in the
context of an investigation into notions of spectrum of noncommutative
$C^*$-algebras.
