11 papers
Extended genus fields of abelian extensions of rational function fields
Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador
In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power deg…
A note on extended genus fields of Kummer extensions of rational function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
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 e…
Function field genus theory for non-Kummer extensions
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
In this paper we first obtain the genus field of a finite abelian non-Kummer --extension of a global rational function field. Then, using that the genus field of a composite of…
Class fields, Dirichlet characters and extended genus fields of global function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
We obtain the extended genus field of an abelian extension of a rational function field. We follow the definition of Anglès and Jaulent, which uses class field theory. First we sho…
Genus fields of Kummer extensions of rational function fields
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
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 o…
Genus fields of Kummer -cyclic extensions
Carlos Daniel Reyes-Morales, Gabriel Villa-Salvador
We give a construction of the genus field for Kummer -cyclic extensions of rational congruence function fields, where is a prime number. First, we compute the genus…