A Generalization of the Artin Theorem

The following Artin theorem about alternative linear algebras defined on the commutative, associative ring with unity is well-known: in an alternative linear algebra, if (a,b,c)=0 , then the subalgebra generated by the elements a , b , and c is associative. In this paper a wide generalization of this classical result is proposed using the concepts of hyperidentity and coidentity. The corresponding universal algebras are referred to as g -algebras.