3 citations · 5 across the 11 of their papers we have counts for
16 papers · 1 filter
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…
Genus fields of global fields
Elizabeth Ramírez-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador
In this paper we obtain the extended genus field of a global field. First we define the extended genus field of a global function field and we obtain, via class field theory, the d…
Genus fields of finite abelian extensions
Jonny Fernando Barreto-Castañeda, Carlos Montelongo-Vázquez, Carlos Daniel Reyes-Morales +2
In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and dete…
Abelian -extensions and additive polynomials
Jonny Fernando Barreto-Castañeda, Fausto Jarquín-Zárate, Martha Rzedowski-Calderón +1
In this work we present some arithmetic properties of families of abelian --extensions of global function fields, among which are their generators and their type of ramification…
Cogalois theory and Drinfeld modules
Marco Antonio Sánchez-Mirafuentes, Julio Cesar Salas-Torres, Gabriel Villa-Salvador
In this paper we generalize the results of \cite{sanchez} to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois the…
Genus Fields of Congruence Function Fields
Myriam Maldonado-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador
Let be a rational congruence function field and consider an arbitrary finite separable extension . If for each prime in ramified in we have that at least one ramif…
Congruence Function Fields with Class Number One
Martha Rzedowski-Calderón, Gabriel Villa-Salvador
We prove that there exists, up to isomorphism, exactly one function field over the finite field of two elements of class number one and genus four. This result, together with the o…
Radical Extensions for the Carlitz--Hayes Module
Marco Sánchez--Mirafuentes, Gabriel Villa--Salvador
Let be a finite extension of congruence function fields. We say that is a {\it radical extension} if is generated by roots of polynomials , where $…
A combinatorial proof of the Kronecker--Weber Theorem in positive characteristic
Julio Cesar Salas-Torres, Martha Rzedowski-Calderón, Gabriel Villa-Salvador
In this paper we present a combinatorial proof of the Kronecker--Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their ar…
Artin--Schreier and Cyclotomic Extensions
Julio Cesar Salas--Torres, Martha Rzedowski--Calderón, Gabriel Villa--Salvador
In this paper we prove that any Artin--Schreier extension of a congruence rational function field is contained in the composite of a cyclotomic function field and a constant field…
Genus fields of abelian extensions of congruence rational function fields
Myriam Maldonado-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador
In the published version of this paper [Finite Fields and Their Applications {\bf 20} (2013) 40--54], there is an error in the proof of Theorem 4.2 of the paper. Here we correct th…