Conditions For Nilpotency Of Hom-Lie Rings

In this thesis,we mainly consider nilpotency of hom-Lie algebras and hom-Lie rings.We reduce the case where the twist map ? is general linear map to the study of involutive hom-Lie algebras,that is,?~2= id.We establish a correspondence of nilpotency between Lie algebras and hom-Lie algebras by building relationships between Lie algebras and hom-Lie algebras.The maximal subalgebras condition for nilpotency of hom-Lie algebras over the filed F is discussed.Moreover,the normalizer condition and the maximal subalgebras condition for nilpotency of hom-Lie rings are investigated.And we obtained the normalizer condition for nilpotency of hom-Lie algebra over the Noetherian ring and the maximal subalgebras condition for nilpotency of hom-Lie algebra over the Jacobson ring.