论文标题
代数posets的代数特性
Algebraic properties of paraorthomodular posets
论文作者
论文摘要
副寄生POSET被部分排序的界定设置，该集合由由量子力学的逻辑 - 代数方法引起的量子结构引起的抗酮相关。本工作的目的是从代数和秩序理论的角度开始对副词的POSET理论进行系统的调查。一方面，我们表明，副词的posets可以通过平滑的代表来接受代数处理，而在有抗反应的界定的界定直接体方面。另一方面，我们根据禁止配置研究了它们的顺序理论特征。此外，提供了抗元素的限制性POSET的充分和必要条件，其Dedekind-Macneille的完成为偏执。
Paraorthomodular posets are bounded partially ordered set with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from an algebraic and order-theoretic perspective. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind-MacNeille completion is paraorthomodular are provided.
