ABSTRACT
Our goal in this section of the text is to discover which integral domains have a unique factorization theorem like the Fundamental Theorem of Arithmetic. That is, we wish to obtain a common generalization of Z and Q[x]. As we shall see, there are two stages to obtain such a unique factorization theorem. First, we need to see whether elements in an arbitrary integral domain can even be factored into irreducibles at all, and then focus our attention on whether such a factorization is unique (up to order and unit factors).
