If P is a prime ideal of a polynomial ring K[x], where K is a field, then P is determined by an irreducible polynomial in K[x]. The purpose of this paper is to show that any prime ideal of a polynomial ring in n-indeterminates over a not necessarily commutative ring R is determined by its intersection with R plus n polynomials.
Proceedings of the American Mathematical Society. Providence, RI. Vol. 125, no. 1 (jan. 1997), p. 67-74.