On the structure of Lie semirings and Lie mappings

The objective of this paper is to characterize the enormous structure of Lie semirings. In the sequel, the Lie ideal structure and Lie mappings are also investigated. Finally, it is proved that in a simple Lie semiring [Formula: see text] with [Formula: see text], [Formula: see text] contains all proper Lie ideals of [Formula: see text] and as a consequence, the simplicity of quotient Lie semiring [Formula: see text] is established.