On the Splitting Ring of a Polynomial

Abstract

Abstract. Let f (Z) = Z n − a 1 Z n−1 + · · · + (−1) n−1 a n−1 Z + (−1) n an be a monic polynomial with coefficients in a ring R with identity, not necessarily commutative. We study the ideal I f of R[X 1 , . . . , Xn] generated by σ i (X 1 , . . . , Xn) − a i , where σ 1 , . . . , σn are the elementary symmetric polynomials, as well as the quotient ring R[X 1 , . . . , Xn]/I f .