On identities in orthocomplemented difference lattices

Milan Matoušek, Pavel Pták
2010 Mathematica Slovaca  
AbstractIn this note we continue the investigation of algebraic properties of orthocomplemented (symmetric) difference lattices (ODLs) as initiated and previously studied by the authors. We take up a few identities that we came across in the previous considerations. We first see that some of them characterize, in a somewhat non-trivial manner, the ODLs that are Boolean. In the second part we select an identity peculiar for set-representable ODLs. This identity allows us to present another
more » ... esent another construction of an ODL that is not set-representable. We then give the construction a more general form and consider algebraic properties of the 'orthomodular support'.
doi:10.2478/s12175-010-0033-7 fatcat:cwvza72w6bg2viooq4tgssfrp4