Quadratic Extensions I: General Concepts and Extensions of ℤ and ℚ

2021 ◽  
pp. 183-220
Author(s):  
Anthony Kay
Keyword(s):  
Quadratic Extensions

Power Integral Bases in Composits of Number Fields

1998 ◽  
Vol 41 (2) ◽  
pp. 158-165 ◽  
Author(s):  
István Gaál
Keyword(s):  
Number Fields ◽  
Parametric Family ◽  
Prime Degree ◽  
Index Form ◽  
Form Equation ◽  
Integral Bases ◽  
Quadratic Extensions ◽  
Totally Real

AbstractIn the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree 10 of this type.

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

On an Exceptional Phenomenon in Certain Quadratic Extensions

1954 ◽  
Vol 6 ◽  
pp. 474-476 ◽  
Author(s):  
H. B. Mann
Keyword(s):  
Cyclic Extension ◽  
Quadratic Extensions ◽  
Image Position

Let Ω be a cyclic extension of degree l over the field Σ. Correcting an error which for some time had been haunting the literature, Hasse (1, p. 272) noted that for l = 2, the field Ω may contain a unit ξ such that.

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