Ideally $\mathcal{J}$-decomposable semigroups

We consider ideally $\mathcal{J}$-decomposable semigroups ($\mathcal{J}$ –— is a system of semigroup identities). It is proved that every ideally $\mathcal{J}$-decomposable semigroup has a $\mathcal{J}$-decomposable series of ideals.