ABSTRACT
In this chapter, R will be a principal ideal domain with quotient field K, and P will be a complete set of nonassociated irreducible elements (cf. Example 2.2.4). Each element x in K* can be written in the form ϵ ∏ p i m i / ∏ q i n i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003210177/074c5e6c-036b-46e6-9fbd-ef8c3dc19390/content/ieq0174.tif"/> , where Pi,qi ∈ P, mi,ni ∈ Z >0, and ∈ is an invertible element of R. Such a representation is unique, as may be seen by equating any two such representations and cross multiplying to clear fractions.
