完全非中心列理想和环中不变加法子群

Eusebio Gardella, Tsiu-Kwen Lee, Hannes Thiel
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引用次数: 0

摘要

我们证明了确保环中的列理想或不变加法子群包含所有加法换元的条件。一个关键的假设是,子群是完全非中心的,也就是说,它在每个商中的映像都是非中心的。对于特性$\neq 2$域上的单值代数,其中每个加法换元都是平方零元素之和,我们证明了当且仅当一个完全非中心子空间在所有内含自动形下不变时,它是一个李理想。这尤其适用于零积平衡代数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fully noncentral Lie ideals and invariant additive subgroups in rings
We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic $\neq 2$ where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras.
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