A subspace H of a Leibniz algebra L is called a quasi-ideal if $[H,K]+[K,H]\subseteq H+K$ for every subspace K of L. It includes ideals and subalgebras of codimension one in L. Quasi-ideals of Lie algebras were classified in two remarkable papers by Amayo. The objective here is to extend those results to the larger class of Leibniz algebras, and to classify those Leibniz algebras in which every subalgebra is a quasi-ideal.

中文翻译：

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莱布尼兹代数的拟理想

子空间ħ一个莱布尼茨代数的大号称为准理想如果$[H，ķ]+[ķ，H]\subseteq H+ķ$每一个子空间ķ的大号。它包括L中的余维之一的理想和子代数。李·代数的拟理想由Amayo在两篇杰出的论文中分类。此处的目的是将这些结果扩展到更大的莱布尼兹代数类别，并对每个子代数都是准理想的莱布尼兹代数进行分类。