Derivation on Vinberg rings

Resumen

A nonassociative ring which contains a well-known associative ring or left symmetric ring also known as Vinberg ring is of great interest. A method to construct Vinberg nonassociative ring is given; Vinberg nonassociative ring  is shown as simple; all the derivations of nonassociative simple Vinberg  algebra defined are determined; and finally in solid algebra it is shown that if  is a nonzero endomorphism of , then  is an epimorphism.