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Genus fields of Kummer ℓn-cyclic extensions
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2021-07-01 , DOI: 10.1142/s0129167x21500622
Carlos Daniel Reyes-Morales 1 , Gabriel Villa-Salvador 1
Affiliation  

We give a construction of the genus field for Kummer n-cyclic extensions of rational congruence function fields, where 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 -cyclic extension. Finally, we study the extension (K1K2)𝔤𝔢/(K1)𝔤𝔢(K2)𝔤𝔢, for K1, K2 abelian extensions of k.

中文翻译:

Kummer ℓn-循环扩展的属域

我们给出了 Kummer 的属域的构造n-有理同余函数域的循环扩展,其中是一个素数。首先,我们计算分圆函数域中包含的域的属域,然后计算一般情况。这概括了 Peng 为 Kummer 获得的结果-循环扩展。最后,我们研究扩展(ķ1ķ2)𝔤𝔢/(ķ1)𝔤𝔢(ķ2)𝔤𝔢, 为了ķ1,ķ2的阿贝尔扩展ķ.
更新日期:2021-07-01
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