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Part of book or chapter of book . 1985 . Peer-reviewed

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Generalized Orthomodular Lattices

Name: Generalized Orthomodular Lattices
Creator: Ladislav Beran

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1985Publisher:Springer Netherlands

Authors: Ladislav Beran;

doi: 10.1007/978-94-009-5215-7_5

Generalized Orthomodular Lattices

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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: (G 1) The algebra ([O,a], ∨, ∧,P(a), 0,a) is an orthomodular lattice for every a∈G. (G 2) For any x ⩽ a ⩽ b of G, xP(a) = xP(b) ∧ a.

Related Organizations

Charles University
Czech Republic

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