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A note on absolute-valued algebras satisfying (xx2)x = x(x2x)
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2021-05-26 , DOI: 10.1142/s0219498822501729
Kandé Diaby 1 , Abdellatif Rochdi 2
Affiliation  

We study the absolute-valued algebras 𝒜 satisfying the identity (xx2)x=x(x2x). We show that, if moreover, the norm of 𝒜 comes from an inner product and 𝒜 contains a nonzero central element then 𝒜 is finite dimensional and isomorphic to either ,, , , , 𝕆, or 𝕆.



中文翻译:

关于满足 (xx2)x = x(x2x) 的绝对值代数的说明

我们研究绝对值代数𝒜满足身份(XX2)X=X(X2X).我们证明,如果此外,𝒜来自内积和𝒜那么包含一个非零中心元素𝒜是有限维和同构的,,*,,*,𝕆, 或者𝕆*.

更新日期:2021-05-26
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