  The goal of this short note is to prove that when $A$ is a closed
*-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property
plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an
isomorphism from the boolean algebra of all regular ideals of $B$ to the
boolean algebra of all regular, invariant ideals of $A$.
