General Theory of Leibniz Algebras

Leonid A. Kurdachenko is a Distinguished Professor in the Department of Algebra and Geometry at Oles Honchar Dnipro National University, Ukraine. He is a prominent leading researcher in algebra and has authored more than 200 peer reviewed journal articles and more than a dozen books dedicated to contemporary topics in modern algebra published by Wiley, CRC, Word Scientific, and others. He was an invited speaker for numerous international algebra conferences and served as visiting professor in many universities in different countries including Germany, Greece, Italy, Spain, USA, and others.Aleksandr A. Pypka is a Professor and Department Chair in the Department of Algebra and Geometry at Oles Honchar Dnipro National University, Ukraine. He is an active researcher in algebra and has authored more than 60 peer reviewed journal articles and a book dedicated to contemporary topics in modern algebra.  He has been an invited speaker in international algebra conferences.Igor Y. Subbotin is a Professor in the Department of Mathematics and Natural Sciences at National University, USA.  He is a recognized expert in algebra and has authored more than 170 peer reviewed journal articles and more than a dozen books dedicated to contemporary topics in modern algebra published by Wiley, CRC, World Scientific and others.  He has served as an invited speaker in many international algebra conferences.

• Elementary Properties and Connections.- Structure of Cyclic Leibniz Algebras.- Leibniz Algebras whose Proper Sub-algebras are Lie Algebras.- Leibniz Algebras whose Proper Sub-algebras are Ideals.- Leibniz Algebras in which the Relation “to be an ideal” is Transitive.- Leibniz Algebras whose Proper Sub-algebras are either Ideals or Contra-ideals.- Influence of Ideals and Self-idealizing Sub-algebras on the Structure of Leibniz Algebras.- Influence of Anti-commutativity on the Structure of Leibniz Algebras.- Analogue of Schur's Theorem and its Generalizations.