 

Paul J. Truman
Integral HopfGalois structures for tame extensions view print


Published: 
October 9, 2013

Keywords: 
HopfGalois structures, HopfGalois module theory, Hopf order, tame ramification 
Subject: 
11R33 (primary), 11S23 (secondary) 


Abstract
We study the HopfGalois module structure of algebraic integers in some Galois extensions of padic fields L/K which are at most tamely ramified, generalizing some of the results of
the author's 2011 paper cited below.
If G=Gal(L/K) and H=L[N]^{G} is a Hopf algebra giving a HopfGalois structure on L/K, we give a criterion for the O_{K}order O_{L}[N]^{G} to be a Hopf order in H. When O_{L}[N]^{G} is Hopf, we show that it coincides with the associated order A_{H} of O_{L} in H and that O_{L} is free over A_{H}, and we give a criterion for a HopfGalois structure to exist at integral level. As an illustration of these results, we determine the commutative HopfGalois module structure of the algebraic integers in tame Galois extensions of degree qr, where q and r are distinct primes.


Author information
School of Computing and Mathematics, Keele University, UK
P.J.Truman@Keele.ac.uk

