
Journal of Lie Theory 31 (2021), No. 4, 9911002 Copyright Heldermann Verlag 2021 On Certain Classes of Algebras in which Centralizers are Ideals Ripan Saha Department of Mathematics, Raiganj University, Raiganj 733134, India ripanjumaths@gmail.com David A. Towers Department of Mathematics and Statistics, Lancaster University, Lancaster, England d.towers@lancaster.ac.uk This paper is primarily concerned with studying finitedimensional anticommutative nonassociative algebras in which every centralizer is an ideal. These are shown to be antiassociative and are classified over a field F of characteristic different from 2; 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. Keywords: Anticommutative algebra, antiassociative algebra, Lie algebra, Leibniz algebra, mockLie algebra, centralizer, nilpotent algebra. MSC: 17A30, 17A32, 17B30. [ Fulltextpdf (108 KB)] for subscribers only. 