Counting generators of normal integral bases

1998 ◽  
Vol 120 (5) ◽  
pp. 1007-1018
Author(s):  
G. R. Everest
Keyword(s):  
Integral Bases

A Note to the Paper on Integral Bases

1958 ◽  
Vol 9 (1) ◽  
pp. 173
Author(s):  
Virginia Hanly ◽  
H. B. Mann
Keyword(s):  
Integral Bases

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 Power Integral Bases in Orders of Composite Fields

2002 ◽  
Vol 11 (1) ◽  
pp. 87-90 ◽  
Author(s):  
István Gaál ◽  
Páter Olajos ◽  
Michael Pohst
Keyword(s):  
Integral Bases

scholarly journals The Maximal Order of Hyper-($b$-ary)-expansions

10.37236/5441 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Michael Coons ◽  
Lukas Spiegelhofer
Keyword(s):  
Recent Result ◽  
Nonnegative Integer ◽  
Maximal Order ◽  
General Integral ◽  
Integral Bases

Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.

scholarly journals Normal integral bases and ray class groups

2004 ◽  
Vol 114 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Humio Ichimura
Keyword(s):  
Class Groups ◽  
Integral Bases
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