论文标题
外观和绝对$ t_1s $ claped的半群
Injectively and absolutely $T_1S$-closed semigroups
论文作者
论文摘要
semigroup $ x $是$ $ $（resp。$ indentively $）$ t_1s $ - $封闭$，如果任何（射击）同构$ h：x \ to y $ to y $ h：x \ to $ t_1 $ t_1 $ topology semigrop $ y \ in \ mathcal c $，image $ h [x] $ in $ y $ y in $ y $。我们证明，当$ x $有界，非语言和clifford-finite时，当时$ t_1s $ closs $ t_1s $被认为是$ t_1s $的。使用此表征，我们证明（1）每个注入$ T_1S $ cluct的半群都具有$ T_1S $ cluct的中心，以及（2）每个绝对$ T_1S $ cluct的半群都有有限的中心。
A semigroup $X$ is $absolutely$ (resp. $injectively$) $T_1S$-$closed$ if for any (injective) homomorphism $h:X\to Y$ to a $T_1$ topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. We prove that a commutative semigroup $X$ is injectively $T_1S$-closed if and only if $X$ is bounded, nonsingular and Clifford-finite. Using this characterization, we prove that (1) every injectively $T_1S$-closed semigroup has injectively $T_1S$-closed center, and (2) every absolutely $T_1S$-closed semigroup has finite center.
