Nonassociative cyclic extensions of fields and central simple algebras
We define nonassociative cyclic extensions of degree m of both fields andcentral 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 d...
| Main Authors: | , |
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| Format: | Article |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53113/ |
| Summary: | We define nonassociative cyclic extensions of degree m of both fields andcentral 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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