scholarly journals Quadratic function fields with exponent two ideal class group

2006 ◽  
Vol 116 (1) ◽  
pp. 21-41 ◽  
Author(s):  
Victor Bautista-Ancona ◽  
Javier Diaz-Vargas
Keyword(s):  
Class Group ◽  
Function Fields ◽  
Quadratic Function ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Function Fields

scholarly journals Imaginary quadratic function fields with ideal class group of prime exponent

2017 ◽  
Vol 173 ◽  
pp. 243-253
Author(s):  
Victor Bautista-Ancona ◽  
Javier Diaz-Vargas ◽  
José Alejandro Lara Rodríguez
Keyword(s):  
Class Group ◽  
Function Fields ◽  
Quadratic Function ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Function Fields ◽  
Prime Exponent

Class Number Divisibility in Real Quadratic Function Fields

1992 ◽  
Vol 35 (3) ◽  
pp. 361-370 ◽  
Author(s):  
Christian Friesen
Keyword(s):  
Class Number ◽  
Function Field ◽  
Class Group ◽  
Quadratic Function ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Function Field ◽  
Quadratic Function Fields ◽  
Real Quadratic ◽  
The Ideal

AbstractLet q be a positive power of an odd prime p, and let Fq(t) be the function field with coefficients in the finite field of q elements. Let denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic . The following theorem is proved: Let n ≧ 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, such that n divides the class number, . The proof constructs an element of order n in the ideal class group.

On l-class groups of global function fields

2016 ◽  
Vol 12 (02) ◽  
pp. 341-356
Author(s):  
Zhengjun Zhao ◽  
Wanbao Hu
Keyword(s):  
Class Group ◽  
Function Fields ◽  
Integral Closure ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Prime Degree ◽  
Global Function ◽  
Global Function Fields ◽  
Genus Theory ◽  
The Ideal

Let [Formula: see text] be a finite geometric separable extension of the rational function field [Formula: see text], and let [Formula: see text] be a finite cyclic extension of [Formula: see text] of prime degree [Formula: see text]. Assume that the ideal class number of the integral closure [Formula: see text] of [Formula: see text] in [Formula: see text] is not divisible by [Formula: see text]. Using genus theory and Conner–Hurrelbrink exact hexagon for function fields, we study in this paper the [Formula: see text]-class group of [Formula: see text] (i.e. the Sylow [Formula: see text]-subgroup of the ideal class group of [Formula: see text]) as Galois module, where [Formula: see text] is the integral closure of [Formula: see text] in [Formula: see text]. The resulting conclusion is used to discuss the relations of class numbers for the biquadratic function fields with their quadratic subfields.

Class number parities of compositum of quadratic function fields

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Sunghan Bae ◽  
Hwanyup Jung
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Ideal Class ◽  
Quadratic Function Fields

AbstractThe parities of ideal class numbers of compositum of quadratic function fields are studied. Especially, the parities of ideal class numbers of

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