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A note on extended genus fields of Kummer extensions of rational function fields

Martha Rzedowski-Calderón, Gabriel Villa-Salvador

Abstract

We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.

A note on extended genus fields of Kummer extensions of rational function fields

Abstract

We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.
Paper Structure (3 sections, 13 theorems, 15 equations)

This paper contains 3 sections, 13 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. General Kummer extensions of $k$
  3. Comparison among various extended genus fields

Key Result

Proposition 2.2

We have that $[J_K:K^*(\Delta\times\prod_{\mathfrak p\nmid\infty}U_{\mathfrak p})]$ is finite.

Theorems & Definitions (26)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Corollary 2.4
  • Proposition 2.5
  • proof
  • Proposition 2.6
  • proof
  • ...and 16 more