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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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