Abstract:The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. $D$-radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of $\mathaccent "705E C$-radicals. In addition, a necessary and sufficient condition for the equality of prime radicals is obtained.
Keywords: semiprime ideal, prime ideal, congruence of a lattice, allele, lattice polynomial, meet-irreducible element, kernel, forbidden exterior quotients, $D$-radical, prime radical
AMS Subject Classification: 06B10