Nonassociative cyclic extensions of fields and central simple algebras |
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Authors: | C. Brown S. Pumplün |
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Affiliation: | School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom |
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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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Keywords: | Primary 17A35 secondary 17A60 16S36 Skew polynomial Ore polynomial Cyclic algebra Cyclic extension |
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