Nonassociative cyclic extensions of fields and central simple algebras
Rings and Algebras
2021-04-13 v1
Abstract
We define nonassociative cyclic extensions of degree m of both fields and central simple algebras over fields. If a suitable field contains a primitive mth (resp., qth) root of unity, we show that suitable nonassociative generalized cyclic division algebras yield nonassociative cyclic extensions of degree m (resp., qs). Some of Amitsur's classical results on non-commutative associative cyclic extensions of both fields and central simple algebras are obtained as special cases.
Keywords
Cite
@article{arxiv.1803.05698,
title = {Nonassociative cyclic extensions of fields and central simple algebras},
author = {Christian Brown and Susanne Pumpluen},
journal= {arXiv preprint arXiv:1803.05698},
year = {2021}
}
Comments
13 pages