Generalizations of the primitive element theorem (Q1178783)

The authors prove several ``primitive element type'' results for separable finitely generated (but not necessarily simple) algebras over infinite fields, and then extend these results to algebras over a commutative local or semilocal ring \(R\) where \(R/M\) is an infinite field for every maximal ideal \(M\). The main result of the paper is that a separable finitely generated algebra \(A\) over an infinite field \(F\) is generated by two elements, i.e. \(A=F[x,y]\) and if A is commutative, \(A=F[x]\).