A class of profinite Hopf-Galois extensions over Q. Issue 6 (3rd June 2018)

• Record Type: Journal Article
• Authors: Kohl, Timothy
• Is Part Of: Communications in algebra. Volume 46:Issue 6(2018)
• Page Start: 2534
• Page End: 2550
• Publication Date: 2018-06-03
• Subjects: Greither-Pareigis theory -- Hopf-Galois extension -- profinite extension; 16W30 -- 12F10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1384001
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: For p >2 prime and a a rational which is not a p n -th power for any n, the extension ℚ ( w n )∕ ℚ where w n = a p n is separable but non-normal. The Hopf-Galois theory for such extensions was determined by Greither and Pareigis, and for radical extensions such as these by the author. In this work, we extend this theory to a class of profinite extensions formed from the union of these finite radical extensions. We construct a "profinite" Hopf algebra which acts satisfying a generalization of a result due to Haggenmüller and Pareigis on Hopf algebra forms of group algebras.