Abstract
We study a special class of lattice-ordered rings and a special radical. We prove that a special radical of an l-ring is equal to the intersection of the right l-prime l-ideals for each of which the following condition holds: the quotient l-ring by the maximal l-ideal contained in a given right l-ideal belongs to the special class. The prime radical of an l-ring is equal to the intersection of the right l-semiprime l-ideals. We introduce the notion of a completely l-prime l-ideal. We prove that N 3(R) is equal to the intersection of the completely l-prime, right l-ideals of an l-ring R, where N 3(R) is the special radical of the l-ring R defined by the class of l-rings without positive divisors of zero.
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