International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 463-470

Generalizations of the primitive element theorem

Christos Nikolopoulos1 and Panagiotis Nikolopoulos2

1Dept. of Computer Science, Bradley University, Peoria 61625, IL, USA
2Department of Mathematics, Michigan State University, E. Lansing 48823, MI, USA

Received 31 July 1990; Revised 21 February 1991

Copyright © 1991 Christos Nikolopoulos and Panagiotis Nikolopoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.