  The purpose of this paper is to introduce a Zariski-like topology on the
spectrum of all proper ideals of a ring. We show that the space is T_0,
quasi-compact, and every irreducible closed subset has a unique generic point.
Furthermore, this space is weaker than a spectral space and if the ring has a
non-trivial idempotent element then the space has a closed disconnected
subspace.
