Non-associative algebras containing the matrix ring Original Research Article

The Lie admissible non-associative algebra image is defined in the papers [Seul Hee Choi, Ki-Bong Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math. 37 (6) (2007) 1813–1830; Seul Hee Choi, Ki-Bong Nam, Weyl type non-associative algebra using additive groups I, Algebra Colloq. 14 (3) (2007) 479–488; Ki-Bong Nam, On Some Non-associative Algebras using Additive Groups, Southeast Asian Bull. Math., vol. 27, Springer-Verlag, 2003, 493–500]. We define in this work the algebra image which generalizes the previous one and is not Lie admissible. We prove that the antisymmetrized Lie algebra image is simple and contains the simple Lie algebra image. We also prove that the matrix ring is embedded in image.