  Let $A$ be a unitary ring and let $(\mathbf{I(A),\subseteq })$ be the lattice
of ideals of the ring $A.$ In this article we will study the property of the
lattice $(\mathbf{I(A),\subseteq})$ to be Noetherian or not, for various types
of rings $A$. In the last section of the article we study certain rings that
are not Boolean rings, but all their ideals are idempotent.
