MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions. (arXiv:1604.05348v2 [math.AC] UPDATED)

An integral domain is said to have the IDF property, when every non-zero element of it, has only a finite number of non-associate irreducible divisors. A counterexample has already been found showing that IDF property does not necessarily ascend in polynomial extensions. In this paper, we introduce a new class of integral domains, called MCD-finite domains, and show that for any domain $D$, $D[X]$ is an IDF domain if and only if $D$ is both IDF and MCD-finite. This in particular entails all the previously known sufficient conditions for the ascent of IDF property. Our new characterization of polynomial domains with IDF property, enables us to use a different construction and build another counterexample which in particular strengthen the previously known result on this matter. 查看全文>>