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arXiv · 2004.12110

On certain classes of algebras in which centralizers are ideals

Ripan Saha·David A. Towers
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Abstract

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.

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Ripan Saha, David A. Towers. 2020-04-25. On certain classes of algebras in which centralizers are ideals. https://arxiv.org/abs/2004.12110

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