Sublattices and $Δ$-blocks of orthomodular posets

Orthomodular posets are algebras over bounded posets with involution

We prove that there is a monadic adjunction between the category of bounded posets with involution and the category of orthomodular posets.

Automorphisms of an orthomodular poset of projections

By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and anti-automorphisms of the lattice L of all closed subspaces of E. A connection between the automorphism group of the ring of all continuous linear mappings defined on E and the automorphism group of the orthoposet Proj(E) is established.

斜正交模与强斜正交模偏序集上的导出算子

Derived operators on skew orthomodular and strong skew orthomodular posets

本文将“sharp”和“flat”运算扩展为斜正交模与强斜正交模偏序集上的算子，推广了可交换关系与换位子，并证明了其重要性质、布尔偏序集下的 Pixley 项三元算子以及合取与蕴涵算子的伴随性。

Varieties corresponding to classes of complemented posets

As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the orthomodular law is satisfied. When we omit the condition that the complementation is an antitone involution, then we obtain skew-orthomodular posets. To each such poset we can assign a bounded lambda-lattice in a non-unique way. Bounded lambda-lattices are lattice-like algebras whose operations are not necessarily associative. We prove that any of the following pr…

与偏序集相关的正交空间

Orthogonality spaces associated with posets

本文为每个偏序集关联一个由真商组成的正交空间，并证明有限有界偏序集是格当且仅当其正交空间逻辑为正交模格，偏序集是链当且仅当该逻辑为布尔代数。