Nonassociative cyclic extensions of fields and central simple algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Brown, C.¹  Pumplun, S.¹ 

[1] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

关键词: Skew polynomial;    Ore polynomial;    Cyclic algebra;    Cyclic extension;   

DOI  :  10.1016/j.jpaa.2018.08.018

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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