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

Truman

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.

Citation

Truman. (2011). Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures

• Acceptance Date: Dec 17, 2011
• Publication Date: Dec 17, 2011
• 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