PRIME IDEALS IN POLYNOMIAL-RINGS IN SEVERAL INDETERMINATES

If P is a prime ideal of a polynomial ring K[x], where K is a field, t hen 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 determin ed by its intersection with R plus n polynomials.