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Genus fields of Kummer extensions of rational function fields
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-10-22 , DOI: 10.1016/j.ffa.2021.101943 Martha Rzedowski-Calderón 1 , Gabriel Villa-Salvador 1
中文翻译:
有理函数域的 Kummer 扩展的属域
更新日期:2021-10-22
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-10-22 , DOI: 10.1016/j.ffa.2021.101943 Martha Rzedowski-Calderón 1 , Gabriel Villa-Salvador 1
Affiliation
In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields. Our main result, the genus of a general Kummer extension of a global rational function field, is a direct consequence of this fact.
中文翻译:
有理函数域的 Kummer 扩展的属域
在本文中,我们获得了全局有理函数域的一般 Kummer 扩展的属域。我们首先研究素数幂的一般 Kummer 扩展的情况。然后我们证明一个具有相对素数的全局有理函数域的两个阿贝尔扩展的复合的属域等于它们各自的属域的复合。我们的主要结果,全局有理函数域的一般 Kummer 扩展的属,是这一事实的直接结果。