Radicals of $l$-rings and special classes of $l$-modules

A special class of lattice-ordered modules is studied. We show that for any special class of $l$-modules we can define a special class of $l$-rings. The special radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-modules over $R$ belonging to the special class. The prime radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-prime $l$-modules over $R$.