半群的直积的可分性
On separability properties in direct products of semigroups
摘要：
研究了与剩余有限性相关的四个有限性条件：完全分离性、强子半群分离性、弱子半群分离性和单演子半群分离性。对于这些性质中的每一个，我们研究在什么条件下该性质在直积下保持不变。我们还考虑了在直积中的因子是否继承了这些性质。给出了有限半群在直积中保持强子半群分离性和单演子半群分离性的充要条件。
英文摘要：
We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.
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。
