ABSTRACT
In this chapter we further explore properties of the integers and by doing so we define some special cases of integral domains. In Section 8.1, we introduce two of these special integral domains called Euclidean domain (ED) and principal ideal domain (PID). In Section 8.2, we introduce the third special integral domain called a unique factorization domain (UFD). In Section 8.3, we look at one particular integral domain which fails to be any of these three special integral domains. One area of study already discussed was to determine which property of a ring R carries over to the corresponding polynomial ring R[x]. In Section 8.4, we prove that the UFD property indeed carries over to the polynomial ring.
