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Some properties of congruence relations on orthomodular lattices. (English) Zbl 1011.06011
Briefly speaking, an orthomodular lattice (OML) is a Boolean algebra where the distributive law is substituted by the weaker orthomodular law \(x\vee y=x\vee((x\vee y)\wedge x')\). The paper under review deals with OMLs. The structure of the lattice of \(p\)-ideals (which are in a bijective correspondence to congruence relations) as well as the structure of congruence classes is investigated. From these results the well-known fact that OMLs are congruence regular, congruence uniform and arithmetical is derived.

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
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