论文标题
kummer属属$ \ ell^n $ -creclic扩展
Genus fields of Kummer $\ell^n$-cyclic extensions
论文作者
论文摘要
我们为kummer $ \ ell^n $ -creclice formations fortaus enformuence函数字段进行了构造，其中$ \ ell $是质量数字。首先，我们计算一个环体函数场中包含的场的属场，然后在一般情况下。这概括了Peng为Kummer $ \ ell $ -Cyclic扩展而获得的结果。最后，我们研究扩展$（k_1k_2）_ {\ frak {ge}}/（k_1）_ {\ frak {ge}}}（k_2）_ {\ frak {ge}} $，$ k_1 $，$ k_1 $，$ k_2 $ k_2 $ abelian Extensions。
We give a construction of the genus field for Kummer $\ell^n$-cyclic extensions of rational congruence function fields, where $\ell$ is a prime number. First, we compute the genus field of a field contained in a cyclotomic function field, and then for the general case. This generalizes the result obtained by Peng for a Kummer $\ell$-cyclic extension. Finally, we study the extension $(K_1K_2)_{\frak{ge}}/(K_1)_{\frak{ge}}(K_2)_{\frak{ge}}$, for $K_1$, $K_2$ abelian extensions of $k$.
