A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p

Details A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p

2009-05-19

arxiv.org/abs/0905.3085v2

Mathematics

Number Theory

11 pages; LaTeX. To appear in Journal de Theorie des Nombres de Bordeaux (special volume, Proceedings of Journees Arithmetique

Scientific paper

Let S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galois for some K-Hopf algebra H. Let D_{S/R} be the different of S/R. We show that if S/R is totally ramified and its degree n is a power of p, then any element $\rho$ of L with $v_L(\rho)$ congruent to $-v_L(D_{S/R})-1$ mod n generates L as an H-module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. Elder for Galois extensions.

Affiliated with

Also associated with

No associations

Rating

A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699782