翻转非关联多项式环和 Cayley-Dickson 构造

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2024-08-30 DOI:10.1016/j.jalgebra.2024.08.021

Masood Aryapoor , Per Bäck

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引用次数: 0

摘要

我们介绍并研究了翻转非关联多项式环。特别是，我们证明了所有 Cayley-Dickson 玻钎都自然地作为这类环的某一类型的商出现；这将复数（和四元数）作为（倾斜）多项式环的商的经典构造扩展到了八元数，甚至更多。我们还将麦克里蒙关于卡伊利-迪克森代数代数性质的一些经典结果扩展到一类翻转非共轭多项式环。

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Flipped non-associative polynomial rings and the Cayley–Dickson construction

We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley–Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (and quaternions) as a quotient of a (skew) polynomial ring to the octonions, and beyond. We also extend some classical results on algebraic properties of Cayley–Dickson algebras by McCrimmon to a class of flipped non-associative polynomial rings.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.