Author(s): Shengxiang WANG, Xiaohui ZHANG, School of Mathematics Sciences, Chuzhou University, Anhui 239000, P. R. China, Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China
Pages: 459-466
Year: 2014 Issue:  4
Journal: Journal of Mathematical Research and Exposition
Keyword:  Hom-associative algebra; Hom-Lie algebra; Kegel’s theorem.;
Abstract: Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra L extending Kegel’s Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra A by showing that any non-commutative Hom-Lie ideal of A must contain [A, A].