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.
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 
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/
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     title = {Remarks on special ideals in lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {607--615},
     year = {1994},
     volume = {35},
     number = {4},
     mrnumber = {1321231},
     zbl = {0812.06002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1994_35_4_a1/}
}
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