On imaginary quadratic function fields with the ideal class group to be exponent ≤2

1998 ◽  
Vol 43 (24) ◽  
pp. 2055-2059
Author(s):  
Weiqun Hu
Keyword(s):  
Class Group ◽  
Function Fields ◽  
Quadratic Function ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Function Fields ◽  
The Ideal

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.

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

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.

Minimal generators of the ideal class group

2021 ◽  
Vol 222 ◽  
pp. 157-167
Author(s):  
Henry H. Kim
Keyword(s):  
Class Group ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Minimal Generators ◽  
The Ideal

On a Theorem of Kawamoto on Normal Bases of Rings of Integers, II

2005 ◽  
Vol 48 (4) ◽  
pp. 576-579 ◽  
Author(s):  
Humio Ichimura
Keyword(s):  
Prime Number ◽  
Number Field ◽  
Class Group ◽  
Natural Homomorphism ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Integral Basis ◽  
Rings Of Integers ◽  
Integer Ring ◽  
The Ideal

AbstractLet m = pe be a power of a prime number p. We say that a number field F satisfies the property when for any a ∈ F×, the cyclic extension F(ζm, a1/m)/F(ζm) has a normal p-integral basis. We prove that F satisfies if and only if the natural homomorphism is trivial. Here K = F(ζm), and denotes the ideal class group of F with respect to the p-integer ring of F.

Circulant Graphs and 4-Ranks of Ideal Class Groups

1994 ◽  
Vol 46 (1) ◽  
pp. 169-183 ◽  
Author(s):  
Jurgen Hurrelbrink
Keyword(s):  
Quadratic Forms ◽  
Class Group ◽  
Number Fields ◽  
Regular Graphs ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Number ◽  
Ideal Class Groups ◽  
Yield Information ◽  
The Ideal

AbstractThis is about results on certain regular graphs that yield information about the structure of the ideal class group of quadratic number fields associated with these graphs. Some of the results can be formulated in terms of the quadratic forms x2 + 27y2, x2 + 32y2, x2 + 64y2.

Sign in / Sign up

Export Citation Format

Share Document