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Article

Beran, Ladislav
On the rhomboidal heredity in ideal lattices. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 4, pp. 723-726
MSC: 06B10, 06C05 | MR 1240194 | Zbl 0782.06007
Keywords:
rhomboidal heredity; principal ideal; semiprime ideal; modular lattice; quotient; allele; relatively complemented lattice; weakly perspective; weakly projective quotients
Summary:
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.
References:
[1] Beran L.: Orthomodular Lattices (Algebraic Approach). Reidel Dordrecht (1985). MR 0784029 | Zbl 0558.06008
[2] Beran L.: On semiprime ideals in lattices. J. Pure Appl. Algebra 64 (1990), 223-227. MR 1061299 | Zbl 0703.06003
[3] Grätzer G. and Schmidt E.T.: On ideal theory for lattices. Acta Sci. Math. 19 (1958), 82-92. MR 0095795
[4] Rav Y.: Semiprime ideals in general lattices. J. Pure Appl. Algebra 56 (1989), 105-118. MR 0979666 | Zbl 0665.06006
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