Leibniz algebras in which all centralizers of nonzero elements are zero algebras

This paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.