Ideal spaces: An extension of structure spaces of rings

Can there be a structure space-type theory for an arbitrary class of ideals ring? The ideal spaces introduced in this paper allows such study and our includes (but not restricted to) prime, maximal, minimal strongly irreducible, completely proper, minimal, primary, nil, nilpotent, regular, radical, principal, finitely generated ideals. We characterise that are sober. introduce the notion disconnected show ring with zero Jacobson containing all maximal imply existence nontrivial idempotent elements ring. also give sufficient condition spectrum to connected.