Geodesic
Remarks on special ideals in lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 607-615.

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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 $\hat C$-radicals. In addition, a necessary and sufficient condition for the equality of prime radicals is obtained.
Classification : 06B10
Keywords: semiprime ideal; prime ideal; congruence of a lattice; allele; lattice polynomial; meet-irreducible element; kernel; forbidden exterior quotients; $D$-radical; prime radical 
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Beran, Ladislav. Remarks on special ideals in lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 607-615. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a1/