adv

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

Solidot 文章翻译

你的名字

留空匿名提交
你的Email或网站

用户可以联系你
标题

简单描述
内容