On identities in orthocomplemented difference lattices

Mathematica Slovaca

Pavel Pták¹  Milan Matoušek¹ 

关键词: orthomodular poset;    quantum logic;    symmetric difference;    Boolean algebra;   

DOI  :  10.2478/s12175-010-0033-7

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In 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 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’.

【 授权许可】

Unknown