On a characterization of the lattice of all ideals of a Boolean ring
Leopoldo Nachbin (1949)
Fundamenta Mathematicae
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Leopoldo Nachbin (1949)
Fundamenta Mathematicae
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Josef Tkadlec (1991)
Colloquium Mathematicae
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We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result...
P. Ribenboin (1969)
Fundamenta Mathematicae
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Jaromír Duda (1990)
Mathematica Slovaca
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František Fiala (1970)
Archivum Mathematicum
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