On Certain Classes of Algebras in which Centralizers are Ideals

Key Points

• The paper aims to classify finite-dimensional anti-commutative nonassociative algebras where every centralizer is an ideal.
• Studied properties of finite-dimensional anti-commutative nonassociative algebras.
• Classified algebras over a field with characteristic different from 2.
• Demonstrated nilpotency and metabelian nature of these algebras.
• Applied findings to prove solvability of Leibniz algebras over characteristic zero fields.
• All examined algebras were found to be nilpotent of class at most 3.
• Classifications revealed that these algebras are metabelian.
• Established that any Leibniz algebra with all centralizers as ideals is solvable.