当前位置: X-MOL 学术Commun. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A short characterization of the octonions
Communications in Algebra ( IF 0.7 ) Pub Date : 2021-07-14 , DOI: 10.1080/00927872.2021.1943425
Erwin Kleinfeld 1 , Yoav Segev 2
Affiliation  

Abstract

In this article, we prove that if R is a proper alternative ring whose additive group has no 3-torsion and whose non-zero commutators are not zero-divisors, then R has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field. We include other characterizations of octonion division algebras and we also deal with the case where (R,+) has 3-torsion.



中文翻译:

八元数的简短描述

摘要

在本文中,我们证明,如果R是一个适当的替代环,其加性群没有 3 扭并且其非零换向子不是零因数,则R没有零因数。根据布鲁克和克莱因菲尔德的定理,如果R的特征不是 2,则R的中心商是某个域上的八元数除法代数。我们包括八元除法代数的其他特征,我们还处理以下情况(电阻,+) 有 3 个扭力。

更新日期:2021-07-14
down
wechat
bug