The Structure Group of a Generalized Orthomodular Lattice

Studia Logica 106 (1):85-100 (2018)
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Abstract

Orthomodular lattices with a two-valued Jauch–Piron state split into a generalized orthomodular lattice and its dual. GOMLs are characterized as a class of L-algebras, a quantum structure which arises in the theory of Garside groups, algebraic logic, and in connections with solutions of the quantum Yang–Baxter equation. It is proved that every GOML X embeds into a group G with a lattice structure such that the right multiplications in G are lattice automorphisms. Up to isomorphism, X is uniquely determined by G, and the embedding \\) is a universal group-valued measure on X.

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Citations of this work

L -effect Algebras.Wolfgang Rump & Xia Zhang - 2020 - Studia Logica 108 (4):725-750.

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References found in this work

Implication connectives in orthomodular lattices.L. Herman, E. L. Marsden & R. Piziak - 1975 - Notre Dame Journal of Formal Logic 16 (3):305-328.

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