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arXiv · 1604.05348

MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions

Sina Eftekhari·Mahdi Reza Khorsandi
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Abstract

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 result entails all the previously known sufficient conditions for the ascent of the IDF property. Our new characterization of polynomial domains with the IDF property enables us to use a different construction and build another counterexample which strengthen the previously known result on this matter.

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Sina Eftekhari, Mahdi Reza Khorsandi. 2016-04-18. MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions. https://doi.org/10.1080/00927872.2018.1424884

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