论文标题
在LCA组中的TFU扩展
On TFU extensions in LCA groups
论文作者
论文摘要
令$ \ ell $为所有本地紧凑的Abelian（LCA）组的类别。令$ g \ in \ ell $和$ h \ subseteq g $。 $ g $的第一个ULM子组用$ g^{（1）} $表示，而$ h $的关闭为$ \ overline {h} $。正确的简短序列$ 0 \ to a \ stackrelϕ {\ to} b \stackrelψ{\ to} c \ to} c \ to} c \ to in $ \ ell $ in $ \ ell $ in $ \ ell $中的$ tfu $扩展\ edline {b^{（1）}} \ stackrel {\overlineψ} {\ to} \ overline {c^{（1）}} \ 0 $是适当的短序列，是$ \ overline c = ϕ = ϕ = ϕ \ idem mid _ _ _ _ { $ \OVERLINEψ=ψ\ MID _ {\ overline {B^{（1）}}}} $。我们在$ tfu $扩展方面介绍了一些结果。另外，我们确定了$ TFU $扩展分配的条件。
Let $\ell$ be the category of all locally compact abelian (LCA) groups. Let $G\in\ell$ and $H\subseteq G$. The first Ulm subgroup of $G$ is denoted by $G^{(1)}$ and the closure of $H$ by $\overline{H}$. A proper short exact sequence $0\to A\stackrelϕ{\to} B\stackrelψ{\to} C\to 0$ in $\ell$ is said to be a $TFU$ extension if $0\to \overline{A^{(1)}}\stackrel{\overlineϕ}{\to} \overline{B^{(1)}}\stackrel{\overlineψ}{\to} \overline{C^{(1)}}\to 0$ is a proper short exact sequence where $\overlineϕ=ϕ\mid_{\overline{A^{(1)}}}$ and $\overlineψ=ψ\mid_{\overline{B^{(1)}}}$. We introduce some results on $TFU$ extensions. Also, we establish conditions under which the $TFU$ extensions split.
