论文标题
posets截面伪组件的扩展
Extension of sectional pseudocomplementation in posets
论文作者
论文摘要
POSET上的截面伪配置（SP汇编）是部分操作$*$，它与每对$（x，y）$的元素相关联，其中$ x \ ge y $，$ x*y $ x*y $的$ x y $ $ x $在the the the the the the the the the the the the [y] $中的$。任何$*$的$*$ of $*$的总计$ \ \ $ \ $ \ the to n to $*$都是扩展的SP组合，被认为是类似于含义的操作。扩展的SP组合已经在半层次和格子上进行了研究。我们描述了具有扩展的SP汇编的几种天然形成的一般POSET类别，即本操作的各自基本特性，表明其他两项已知的隔离此类类别的尝试实际上并不十分正确，并提出了适当的改进。
Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation $*$ which associates with every pair $(x,y)$ of elements, where $x \ge y$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total extension $\to$ of $*$ is said to be an extended sp-complementation and is considered as an implication-like operation. Extended sp-complementations have already be studied on semilattices and lattices. We describe several naturally arising classes of general posets with extended sp-complementation, present respective elementary properties of this operation, demonstrate that two other known attempts to isolate particular such classes are in fact not quite correct, and suggest suitable improvements.
