论文标题
伪安装的Posets的过滤器和理想
Filters and ideals in pseudocomplemented posets
论文作者
论文摘要
我们研究POSET和伪安装的POSET的理想和过滤器，并显示了分离定理的版本，该版本在此一般环境中以晶格和半层次中的理想和过滤器而闻名。我们扩展了Rao已经引入的 *理想的概念，用于伪造的分布晶格，以及Talukder，Chakraborty和Begum的伪造半层次的概念。我们得出了这种理想的几个重要特性。尤其是，我们解释了主要过滤器，超滤器，满足 *条件和密集元素的过滤器之间的联系。最后，我们证明了 *理想的分离定理。
We study ideals and filters of posets and of pseudocomplemented posets and show a version of the Separation Theorem, known for ideals and filters in lattices and semilattices, within this general setting. We extend the concept of a *-ideal already introduced by Rao for pseudocomplemented distributive lattices and by Talukder, Chakraborty and Begum for pseudocomplemented semilattices to pseudocomplemented posets. We derive several important properties of such ideals. Especially, we explain connections between prime filters, ultrafilters, filters satisfying the *-condition and dense elements. Finally, we prove a Separation Theorem for *-ideals.
