Abstract

This paper, in the area of Commutative Algebra, deals with the ring of polynomials over the ring of integers, denoted Z[x]. I have determined that all non-zero prime ideals in Z[x] are structured in one of three ways. This structure depends on whether the intersection of the ideal with the integers is equal to an ideal generated by a prime integer or is equal to an ideal generated by zero, and the presence or absence of a monic polynomial.