International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 463-470
Generalizations of the primitive element theorem
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.