Skip to main content

Research Repository

Advanced Search

Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures

Truman

Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures Thumbnail


Authors



Abstract

We study the nonclassical Hopf-Galois module structure of rings of algebraic integers in some extensions of p-adic fields and number fields which are at most tamely ramified. We show that if L/K is an unramified extension of p-adic fields which is H-Galois for some Hopf algebra H then OL is free over its associated order AH in H. If H is commutative, we show that this conclusion remains valid in ramified extensions of p-adic fields if p does not divide the degree of the extension. By combining these results we prove a generalisation of Noether's theorem to nonclassical Hopf-Galois structures on domestic extensions of number fields.

Acceptance Date Dec 17, 2011
Publication Date Dec 17, 2011
Publicly Available Date Mar 28, 2024
Journal New York Journal of Mathematics
Print ISSN 1076-9803
Pages 799-810
Keywords Noether's theorem, Hopf-Galois structures, domestic extensions
Publisher URL http://nyjm.albany.edu/j/2011/17-34.html

Files

P Truman - Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures.pdf (309 Kb)
PDF




You might also like



Downloadable Citations