The radical in a finitely generated P. I. algebra
Amiram Braun · Bulletin of the American Mathematical Society · 1982
Let R be an associative ring over a commutative ring A, p{X lf ..., X e } a polynomial on the free noncommuting variables X x , ..., X e9 with coefficients in A where one of its coefficient is +1.We say that R is a P.I. (polynomial identity) ring satisfying p{X x , ..., X e } if p(r x , ..., r e ) = 0 for all r v ..., r e in R.We have the following THEOREM A. Let R = A{x lf ..., x k } be a p.i. ring, where A is a noetherian subring of the center Z(R) of R