Let p be a prime number. In this paper we use an old technique of Ø. Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by p-regular equations. To illustrate the potential applications of this construction, we derive from this result an explicit description of a p-integral basis of an arbitrary quartic field in terms of a defining equation. © 2012 World Scientific Publishing Company.
|Journal||Journal of Algebra and its Applications|
|Publication status||Published - 1 Aug 2012|
- Newton polygon
- p-integral basis
- quartic field