Nonassociative cyclic extensions of fields and central simple algebras

被引：7

作者：

Brown, C. ^{[1
]}

Pumplun, S. ^{[1
]}

机构：

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

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2019年 / 223卷 / 06期

关键词：

Skew polynomial; Ore polynomial; Cyclic algebra; Cyclic extension; AUTOMORPHISMS;

D O I：

10.1016/j.jpaa.2018.08.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：2401 / 2412

页数：12

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