the strongly irreducible dimension of rings vs. the derived dimension of the space of strongly irreducible ideals with v-topology

An ideal $i$ of a ring $r$ is called strongly irreducible ideal (si-ideal, for short), whenever the inclusion $jcap ksubseteq i$, implies that $jsubseteq i$ or $ksubseteq i$. let $x={rm sspec}(r)$ be the set of all strongly irreducible ideals of a ring $r$. then $x$ with certain topology has derived dimension if and only if $r$ has strongly irreducible dimension. moreover, the two dimensions differ by at most $1$.