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Remarks on special ideals in lattices. (English) Zbl 0812.06002
Summary: The author studies some characteristic properties of semiprime ideals. Semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. \(D\)-radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of \(\widehat{C}\)- radicals. In addition, a necessary and sufficient condition for the equality of prime radicals is obtained.
MSC:
06B10 Lattice ideals, congruence relations
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