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

Abstract

Special classes of lattice-ordered rings (l-rings) are studied and for special radicals of l-rings the Anderson-Divinsky-Sulinski lemma is proved, i.e., it is proved that if ρ is a special radical in the class of l-rings and I is an l-ideal of an l-ring R, then ρ(I) is an l-ideal of the l-ring R and ρ(I) = ρ(R) ∩ I.