rhomboidal heredity; principal ideal; semiprime ideal; modular lattice; quotient; allele; relatively complemented lattice; weakly perspective; weakly projective quotients
We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.
 Grätzer G. and Schmidt E.T.: On ideal theory for lattices
. Acta Sci. Math. 19 (1958), 82-92. MR 0095795