论文标题
在某些类别的代数中，中央化是理想的
On certain classes of algebras in which centralizers are ideals
论文作者
论文摘要
本文主要涉及研究每个centralizer都是理想的有限维抗共同辅助代数。这些被证明具有反社会性，并被分类为一般字段$ f $；特别是，它们最多是$ 3 $和Metabelian的班级。然后将这些结果应用于表明在特征零字段上的leibniz代数，在该字段中，所有中心化都是理想的。
This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in particular, they are nilpotent of class at most $3$ and metabelian. These results are then applied to show that a Leibniz algebra over a field of charactersitic zero in which all centralizers are ideals is solvable.
