分段伪可补格和偏序集上的滤子和同余
Filters and congruences in sectionally pseudocomplemented lattices and posets
摘要：
在我们以前的论文中，我们与J. Paseka一起介绍了所谓的分段伪补格和偏序集，并阐明了它们在代数构造中的作用。我们相信-类似于相对伪补格-这些结构可以作为某些直觉主义逻辑的代数语义。本文的目的是在这些结构中定义同余和滤子，导出它们之间的相互关系，并描述强分段伪补偏序集中同余的基本性质。对于分段伪补格和偏序集上滤子的描述，我们使用了A。Ursini，即理想的条件和封闭性与他们有关。它似乎是一些有趣的是，一个类似的机器也可以适用于强节伪补偏序集，尽管事实上，相应的理想项并不处处定义。
英文摘要：
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented lattices - these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters both in sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e. ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
