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Аннотация: In this paper, we introduce the notion of an l-prime l-ideal and that of a right l-semiprime l-ideal. We prove that our definitions coincide with the definitions of M. A. Shatalova in the case of two-sided l-ideals. Our main results are the following ones. The radical of an l-ring can be represented as the intersection of the right l-ideals for each of which the following condition holds: the quotient ring by the maximal l-ideal contained in the given right l-ideal is semisimple. The hypernilpotent radical of an l-ring can be represented as the intersection of the right l-semiprime ideals satisfying the same condition.