International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 463-470
doi:10.1155/S0161171291000637
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
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.