Classification of certain non-simple C*-algebras

It is proved that the lattice of closed, two-sided ideals in a C*-algebra c lassifies the class of unital C*-algebras which are inductive limits of seq uences of finite direct sums of C([0, i]) x O-2 End have totally ordered la ttice of ideals, up to *-isomorphism. Furthermore, it is proved that if the lattice of ideals of a separable, uni tal C*-algebra is totally ordered, then it is compact metrizable and has an isolated maximum in the order topology. Conversely, each totally ordered s pace (containing at least two points) which is compact metrizable and has a n isolated maximum in the order topology appears as the lattice of ideals o f a C*-algebra which is an inductive limit of a sequence of finite direct s ums Of C([0, 1]) x O-2.