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

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 V{cal V} is generated by a class of algebras F{cal F}, then the variety of V{cal V}-composition algebras is generated by the class of all full function algebras on direct products of finitely many copies of algebras in F{cal F}.