论文标题
辅助posets中的C理想
c-ideals in complemented posets
论文作者
论文摘要
在他们最近的关于Posets的论文中，第一位作者和第三作者表示的伪弥补，介绍了一个 * - 理想的概念。实际上，这个概念是几位作者在分布式伪配件和半层次中引入的类似概念的扩展，请参见参考文献。现在，我们将这种c理想（双重，c滤波器）的概念应用于补充的posets，在互补既不是抗酮也不是抗事的，但仍然满足某些弱条件。我们在这样的poset中分别显示理想或过滤器分别是c理想或c滤波器，我们证明了它们的基本特性。最后，我们证明了C-Ideals的所谓分离定理。文本以几个示例说明。
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, respectively, and we prove basic properties of them. Finally, we prove so-called Separation Theorems for c-ideals. The text is illustrated by several examples.
