论文标题
矫形和广义的矫正式POSET
Orthomodular and generalized orthomodular posets
论文作者
论文摘要
我们证明，论文中描述的18个元素的非晶格矫形器是最小的，并且是同构的独特之处。由于并非每个布尔式Poset都是矫形器，因此我们考虑了前一篇论文中第一和第三作者引入的所谓的广义矫正posets的类别。我们表明，该类别包含所有布尔式Posets，我们研究其子类由水平的布尔posets组成。为此，我们介绍了兼容性关系的概念和两个要素的所谓换向器。我们展示了这些概念之间的关系，并介绍了这些posets的三元歧视者的概念。本文中包括了许多示例来照明这些概念和结果的例子。
We prove that the 18-element non-lattice orthomodular poset depicted in the paper is the smallest one and unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of the so-called generalized orthomodular posets introduced by the first and third author in a previous paper. We show that this class contains all Boolean posets and we study its subclass consisting of horizontal sums of Boolean posets. For this purpose we introduce the concept of a compatibility relation and the so-called commutator of two elements. We show the relationship between these concepts and we introduce the notion of a ternary discriminator for these posets. Numerous examples illuminating these concepts and results are included in the paper.
