The Variety of Near-Rings is Generated by Its Finite Members

摘要

We show that the variety of near-rings and the variety of zero-symmetric near-rings are both generated by their finite members. We show this in a more general context: if a variety ${cal V}$ is generated by a class of algebras ${cal F}$ , then the variety of ${cal V}$ -composition algebras is generated by the class of all full function algebras on direct products of finitely many copies of algebras in ${cal F}$ .