Special classes of $l$-rings and Anderson–Divinsky–Sulinski lemma

If $\rho$ is a radical in the class of rings and $I$ is an ideal of a ring $R$, then $\rho(I)$ is an ideal of $R$ (the Anderson–Divinsky–Sulinski lemma). Let $\rho$ be a special radical in the class of $l$-rings (lattice-ordered rings) and $I$ be an $l$-ideal of an $l$-ring $R$. In this paper we prove that $\rho(I)$ is an $l$-ideal of the $l$-ring $R$ and $\rho(I)=\rho(R)\cap I$.