Embedding of orthoposets into orthocomplete posets

Rok, strany: 1993, 7 - 12

In this paper we deal with the embedding of an orthoposet into an orthocomplete poset, i.e., into an orthoposet in what there exists the supremum of any set of pairwise orthogonal elements. This embedding is constructed using a restriction of the well-known MacNeille completion. We show a necessary and sufficient condition for preserving the property of orthomodularity. There is given an example of an orthomodular poset, which possesses an orthomodular orthocompletion, but its MacNeille completion is not orthomodular. Besides, we give an example of an orthomodular poset, whose orthocompletion is not orthomodular.

ISO 690:

Palko, V. 1993. Embedding of orthoposets into orthocomplete posets. In Tatra Mountains Mathematical Publications, vol. 3, no.2, pp. 7-12. 1210-3195.

APA:

Palko, V. (1993). Embedding of orthoposets into orthocomplete posets. Tatra Mountains Mathematical Publications, 3(2), 7-12. 1210-3195.