AI 中文总结
本文针对交换充足部分半群，从代数与动力学角度研究准中心集，给出幂等超滤子元素的动力学刻画并探讨其极小动力系统。
AI 中文摘要
H.弗斯滕伯格利用拓扑动力学工具引入了中心集的概念，并建立了著名的中心集定理。满足该定理结论的集合称为C-集。欣德曼、马莱基和施特劳斯首次提出了一类重要的非中心C-集，即准中心集。2017年，A.戈什对交换充足部分半群中的C-集进行了组合处理，其中C-集是满足交换充足部分半群下中心集定理结论的集合。本工作针对交换充足部分半群，从代数和动力学角度探讨准中心集，给出了交换充足部分半群上幂等超滤子元素的动力学刻画，还研究了充足部分半群的极小动力系统。
英文摘要
Using tools from topological dynamics, H.~Furstenberg introduced the notion of \emph{central sets} and established the celebrated Central Sets Theorem. The sets which satisfy the conclusion of the Central Sets Theorem are called $C$-sets. Hindman, Maleki, and Strauss first brought the concept of an important type of $C$-sets called the quasi-central sets which are not central sets. In 2017, A. Ghosh gave the combinatorial treatment of $C$-sets in commutative adequate partial semigroups, where $C$-sets are the sets which satisfy the conclusion of Central Sets Theorem for commutative adequate partial semigroups. In this work, we discuss the Quasi-central sets algebraically and dynamically for commutative adequate partial semigroups. We give dynamical characterization of members of idempotent ultrafilters for commutative adequate partial semigroups, also we study the minimal dynamical systems for an adequate partial semigroup.
