Tekebay A.2026-09-092026-09-092026Tekebay A / 3-nil alternative, pre-Lie and assosymmetric operads / SDU University / Department of Mathematics and Natural Scienceshttps://repository.sdu.edu.kz/handle/123456789/2653An algebra is called alternative if it satisfies the following identities: (ab)c − a(bc) = −(ac)b + a(cb), (ab)c − a(bc) = −(ba)c + b(ac). In this dissertation, we consider free alternative algebra with the additional identity x 3 = 0. For motivation, we refer to the dual operad of the alternative operad. Also, we obtain pre-Lie algebra with the identity x 3 = 0 from binary perm algebra. Finally, we consider assosymmetric algebra with identity x 3 = 0enAnti-Leibniz algebrasThe variety of alternative algebrasKoszul dual operadThesis