论文标题
内部封闭的交换性半群
Injectively closed commutative semigroups
论文作者
论文摘要
令$ \ Mathcal C $为一类拓扑半群。 semigroup $ x $是$ $ $ $ $ \ \ \ natcal c $ - $封闭$，如果$ x $在每个拓扑semigroup $ y \ in \ mathcal c $ in \ mathcal c $中，含有$ x $作为subsemigroup。令$ \ mathsf {t _ {\！2} s} $（resp。$ \ mathsf {t _ {\！z} s} $）是hausdorff（和零维）拓扑半群的类别。我们证明，交换性的半群$ x $是$ \ mathsf {t _ {\！2} s} $ - 当时闭合，并且仅当$ x $被浸入$ \ mathsf {t _ {t _ {\！z} s} s} s} s} $ - 仅如果$ x $ bunded and bolded bunded byed，chainefended bunded，bynefed and x $ bunded bolded，caine-finite，chain-finite，group-siff and cliff and n nest and cliff and cliff。
Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is $injectively$ $\mathcal C$-$closed$ if $X$ is closed in each topological semigroup $Y\in\mathcal C$ containing $X$ as a subsemigroup. Let $\mathsf{T_{\!2}S}$ (resp. $\mathsf{T_{\!z}S}$) be the class of Hausdorff (and zero-dimensional) topological semigroups. We prove that a commutative semigroup $X$ is injectively $\mathsf{T_{\!2}S}$-closed if and only if $X$ is injectively $\mathsf{T_{\!z}S}$-closed if and only if $X$ is bounded, chain-finite, group-finite, nonsingular and not Clifford-singular.
