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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 [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
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