Truman, PJ (2019) Hopf-Galois module structure of tamely ramified radical extensions of prime degree. Journal of Pure and Applied Algebra. (In Press)

[img] Text
HGMS of tamely ramified radical extensions of prime degree RESUBMISSION.pdf - Accepted Version
Restricted to Repository staff only until 11 September 2020.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (296kB)

Abstract

Let K be a number field and let L/K be a tamely ramified radical extension of prime degree p. If K contains a primitive p th root of unity then L/K is a cyclic Kummer extension; in this case the group algebra K[G] (with G = Gal(L/K)) gives the unique Hopf-Galois structure on L/K, the ring of algebraic integers OL is locally free over OK[G] by Noether’s theorem, and G´omez Ayala has determined a criterion for OL to be a free OK[G]-module. If K does not contain a primitive p th root of unity then L/K is a separable, but non-normal, extension, which again admits a unique Hopf-Galois structure. Under the assumption that p is unramified in K, we show that OL is locally free over its associated order in this Hopf-Galois structure and determine a criterion for it to be free. We find that the conditions that appear in this criterion are identical to those appearing in G´omez Ayala’s criterion for the normal case.

Item Type: Article
Additional Information: The final version of this accepted manuscript will be available online at https://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/
Uncontrolled Keywords: Hopf-Galois structure, Hopf-Galois module theory, Galois module structure, Associated order
Subjects: R Medicine > R Medicine (General)
R Medicine > RA Public aspects of medicine
Divisions: Faculty of Natural Sciences > School of Chemical and Physical Sciences
Depositing User: Symplectic
Date Deposited: 12 Sep 2019 08:05
Last Modified: 20 Sep 2019 08:15
URI: http://eprints.keele.ac.uk/id/eprint/6810

Actions (login required)

View Item View Item