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arXiv · 1803.05698

Nonassociative cyclic extensions of fields and central simple algebras

Christian Brown·Susanne Pumpluen
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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.

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Christian Brown, Susanne Pumpluen. 2018-03-15. Nonassociative cyclic extensions of fields and central simple algebras. https://doi.org/10.1016/j.jpaa.2018.08.018

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