Abstract
Let ‵G = (G, ∨, ∧) be a lattice with the least element 0. For any a∈G, define P(a): [0,a]→[0,a],to be a unary operation on [O,a] such that P(a):x↦xP(a). We shall say that ‵G is a generalized orthomodular lattice if and only if it satisfies the following conditions:
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(G 1)
The algebra ([O,a], ∨, ∧,P(a), 0,a) is an orthomodular lattice for every a∈G.
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(G 2)
For any x ⩽ a ⩽ b of G, xP(a) = xP(b) ∧ a.
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© 1985 Ladislav Beran, Prague
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Beran, L. (1985). Generalized Orthomodular Lattices. In: Orthomodular Lattices. Mathematics and Its Applications (East European Series), vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5215-7_5
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DOI: https://doi.org/10.1007/978-94-009-5215-7_5
Publisher Name: Springer, Dordrecht
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