Genus fields of Kummer extensions of rational function fields |
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Affiliation: | 1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;2. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy |
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Abstract: | 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. |
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Keywords: | Global fields Genus fields Kummer extensions Cyclic extensions |
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