仿正交模偏序集的代数性质
Algebraic properties of paraorthomodular posets
摘要：
仿正交模偏序集是由量子力学的逻辑代数方法中的量子结构诱导的具有反调对合的有界偏序集。本工作的目的是从代数和序理论的角度对仿正交模偏序集理论进行系统的研究。一方面，我们表明，paraorthomodular偏序集是顺从的代数处理，通过一个光滑的表示有界directoid与反调对合。另一方面，我们研究了它们在禁戒构型方面的序理论特征。此外，给出了有界偏序集具有反序对合的Dedekind-MacNeille完备化是仿正交模的充分和必要条件.
英文摘要：
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.
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