Prime ideals in polynomial rings in several indeterminates

Abstract:

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.