Generalizations of the primitive element theorem

Abstract

In this paper we generalize the primitive element theorem to the generation of separable algebras over fields and rings. We prove that any finitely generated separable algebra over an infinite field is generated by two elements and if the algebra is commutative it can be generated by one element. We then derive similar results for finitely generated separable algebras over semilocal rings.

Keywords

• generation of algebras
• separable algebras
• semilocal rings.