Nonassociative cyclic extensions of fields and central simple algebras
arXiv:1803.05698 · doi:10.1016/j.jpaa.2018.08.018
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.
arXiv comment13 pages
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