论文标题
$ {\ rm sl} _n $用于全局函数字段和$ n \ geq 3 $
Elementary bounded generation for ${\rm SL}_n$ for global function fields and $n\geq 3$
论文作者
论文摘要
本文表明，组$ {\ rm sl} _n（r）$是针对$ n \ geq 3 $和$ r $的基本生成的，而$ r $是全球函数字段中代数整数的环。与以前的数字字段陈述和全局功能字段的早期陈述相反，在此预印刷中证明的基础界限生成的界限与基础全局函数字段无关，并且仅取决于将我们的主要结果与较早的结果组合在一起的整数$n。$，我们进一步确定，基本界限始终依赖于$ n $ n $ n的全局界限，仅依赖于全球字段。
This paper shows that the group ${\rm SL}_n(R)$ is boundedly elementary generated for $n\geq 3$ and $R$ the ring of algebraic integers in a global function field. Contrary to previous statements for number fields and earlier statements for global function fields, the bounds proven in this preprint for elementary bounded generation are independent of the underlying global function field and only depend on the integer $n.$ Combining our main result with earlier results, we further establish that elementary bounded generation always has bounds independent from the global field in question, only depending on $n.$
