## Milan Matoušek, Pavel Pták

*Symmetric difference on orthomodular lattices and $Z_2$-valued states*

Comment.Math.Univ.Carolin. 50,4 (2009) 535-547.**Abstract:**The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference\,? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_2$-valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.

**Keywords:** orthomodular lattice, quantum logic, symmetric difference, Boolean algebra, group-valued state

**AMS Subject Classification:** 06A15 03G12 28E99 81P10

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