an:00733090
Zbl 0812.06002
Beran, Ladislav
Remarks on special ideals in lattices
EN
Commentat. Math. Univ. Carol. 35, No. 4, 607-615 (1994).
00024674
1994
j
06B10
prime ideal; congruence; allele; lattice polynomial; kernel; forbidden exterior quotients; distributive lattices; semiprime ideals; modular lattices; \(D\)-radicals; prime radicals
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.