On Certain Classes of Algebras in which Centralizers are Ideals

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 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.