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Semiprime ideals in orthomodular lattices. (English) Zbl 0655.06008
A semiprime ideal in a lattice L is a (lattice) ideal I satisfying for all a,b,c\(\in L\), if \(a\wedge b\), \(a\wedge c\in I\) then \(a\wedge (b\vee c)\in I\). The author investigates semiprime ideals in orthomodular lattices (OMLs) and some elementary connections with distributivity and congruence relations. Amongst these are: (i) I is semiprime iff I contains the ideal generated by the commutators of L. (ii) I is semiprime iff I is the intersection of prime ideals. The paper closes with several conditions which characterize semiprime and orthomodular (or p-)ideals in an OML.
Reviewer: M.Roddy

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
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