论文标题
绝对封闭的单体半群
Categorically closed unipotent semigroups
论文作者
论文摘要
令$ \ Mathcal C $为$ T_1 $拓扑半群，包含所有Hausdorff零维拓扑半群。如果$ x $在\ Mathcal c $中关闭$ x $，则$ x $是$ \ mathcal c $ - $关闭$，其中包含$ x $作为离散的subsemigroup; $ x $ IS $ IS $ $ $ $ \ MATHCAL C $ - $封闭$如果任何（注射）同构$ H：X \ to y $ to y $ to topology semigroup $ y \ in \ Mathcal c $，则图像$ h [x] $在$ y $中封闭。如果包含唯一的愿望，则半群$ x $是$ Unipitent $。我们证明，当$ x $ c $ c $ c $ c $ c $ c $时，并且仅当$ x $有界，非单调性（和群 - 芬太尼）时，一个单一的交换性semigroup $ x $是（iNjectife）$ \ mathcal c $ clucked。该表征意味着，对于每一个注入$ \ MATHCAL C $ cLUCT的单位semigroup $ x $，中心$ z（x）$均为$ \ mathcal c $ co $。
Let $\mathcal C$ be a class of $T_1$ topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup $X$ is $\mathcal C$-$closed$ if $X$ is closed in any topological semigroup $Y\in\mathcal C$ that contains $X$ as a discrete subsemigroup; $X$ is $injectively$ $\mathcal C$-$closed$ if for any (injective) homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. A semigroup $X$ is $unipotent$ if it contains a unique idempotent. We prove that a unipotent commutative semigroup $X$ is (injectively) $\mathcal C$-closed if and only if $X$ is bounded, nonsingular (and group-finite). This characterization implies that for every injectively $\mathcal C$-closed unipotent semigroup $X$, the center $Z(X)$ is injectively $\mathcal C$-closed.
