zbMATH — the first resource for mathematics

On semiprime ideals in lattices. (English) Zbl 0703.06003
The author characterizes semiprime ideals in lattices as follows. Theorem. An ideal I of a lattice L is semiprime if and only if there exists no allele p/i with \(i\in I\) and \(p\not\in I\). The author uses this theorem to study when sectionally complemented lattices are distributive.
Reviewer: T.B.Muenzenberger
06B10 Lattice ideals, congruence relations
Full Text: DOI
[1] Beran, L., Orthomodular lattices (algebraic approach), (1985), Reidel Dordrecht · Zbl 0558.06008
[2] Beran, L., Distributivity in finitely generated orthomodular lattices, Comment. math. univ. carolinae, 28, 3, 433-435, (1987) · Zbl 0624.06008
[3] Chevalier, G., Semiprime ideals in orthomodular lattices, Comment. math. univ. carolinae, 29, 2, 379-386, (1988) · Zbl 0655.06008
[4] Rav, Y., Semiprime ideals in general lattices, J. pure appl. algebra, 56, 105-118, (1989) · Zbl 0665.06006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.