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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
MSC:
06B10 Lattice ideals, congruence relations
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References:
[1] Beran, L., Orthomodular lattices (algebraic approach), (1985), Reidel Dordrecht · Zbl 0558.06008
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[4] Rav, Y., Semiprime ideals in general lattices, J. pure appl. algebra, 56, 105-118, (1989) · Zbl 0665.06006
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