Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions

Truman, Paul

Abstract

Let L/K be a finite Galois extension of local or global fields in any characteristic with nonabelian Galois group G, and let be an ambiguous ideal of L. We show that is free over its associated order in K[G] if and only if it is free over its associated order in the Hopf algebra giving the canonical nonclassical Hopf-Galois structure on the extension.

Citation

Truman, P. (2016). Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, 1119 - 1130. https://doi.org/10.1080/00927872.2014.999930

• Acceptance Date: Aug 11, 2014
• Publication Date: Jan 29, 2016
• Journal: Communications in Algebra
• Print ISSN: 0092-7872
• Publisher: Taylor and Francis
• Pages: 1119 - 1130
• DOI: https://doi.org/10.1080/00927872.2014.999930
• Keywords: Associated Order; Galois module structure;Hopf-Galois module theory; Nonabelian extension
• Publisher URL: http://www.tandfonline.com/doi/abs/10.1080/00927872.2014.999930