2020/04/25 by Ripan Saha, Saha, Ripan, David A. Towers +1
Mathematics · #17A30 #17A32 #17B30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2004.12110
openalex publication_date 2020/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.