论文标题
弱继承人，coheirs和Ellis Semigroups
Weak heirs, coheirs and the Ellis semigroups
论文作者
论文摘要
假设$ g \ prec h $是组，$ {\ cal a} \ subseteq {\ cal p}（g），\ {\ cal b} \ subseteq {\ cal p}（h）$是左组转换下关闭的集合的代数。在一些其他假设下，我们发现$ g $ -Flow $ s（{\ cal a}）$的Ellis [semi]组之间的代数连接与$ h $ -flow $ s（{\ cal b}）$。我们将这些结果应用于模型理论环境。也就是说，假设$ g $是在型号$ m $和$ m \ prec^* n $中定义的组。使用弱继承人和弱的coheirs，我们指出了Ellis Semigroups $ S_ {Ext，G}（M）$和$ S_ {Ext，G}（N）$之间的一些代数连接。假设$ s_ {ext，g}（n）$中的每一个最小的理想是我们证明$ s_ {ext，g}（m）$的Ellis组对$ s_ {ext，g}（n）$的Ellis组的封闭子组的同构是同构。
Assume $G\prec H$ are groups and ${\cal A}\subseteq{\cal P}(G),\ {\cal B}\subseteq{\cal P}(H)$ are algebras of sets closed under left group translation. Under some additional assumptions we find algebraic connections between the Ellis [semi]groups of the $G$-flow $S({\cal A})$ and the $H$-flow $S({\cal B})$. We apply these results in the model theoretic context. Namely, assume $G$ is a group definable in a model $M$ and $M\prec^* N$. Using weak heirs and weak coheirs we point out some algebraic connections between the Ellis semigroups $S_{ext,G}(M)$ and $S_{ext,G}(N)$. Assuming every minimal left ideal in $S_{ext,G}(N)$ is a group we prove that the Ellis groups of $S_{ext,G}(M)$ are isomorphic to closed subgroups of the Ellis groups of $S_{ext,G}(N)$.
