论文标题
关于分离群的可分离性有限条件
On separability finiteness conditions in semigroups
论文作者
论文摘要
以剩余的有限性为起点，我们考虑了三种相关的有限属性：弱的子群的可分离性，强大的子群的可分离性和完全的可分离性。我们研究了这些属性中的每一个是否均由Schützenberger组遗传。本文的主要结果指出，对于有限生成的交换性半群$ s $，这三个可分离性条件重合，相当于每一个$ \ nathcal {h} $ - $ s $ of $ s $都是有限的。我们还提供了示例，以表明这些特性通常在交换性半群和有限生成的半群中不同。对于有限许多$ \ Mathcal {H} $ - 类的半群，我们调查它是否具有这些属性之一，并且仅当其所有Schützenberger组都具有该属性时。
Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is inherited by Schützenberger groups. The main result of this paper states that for a finitely generated commutative semigroup $S$, these three separability conditions coincide and are equivalent to every $\mathcal{H}$-class of $S$ being finite. We also provide examples to show that these properties in general differ for commutative semigroups and finitely generated semigroups. For a semigroup with finitely many $\mathcal{H}$-classes, we investigate whether it has one of these properties if and only if all its Schützenberger groups have the property.
