Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into irreducibles. En route to these characterizations, we show that this construction yields a domain with infinite restricted elasticity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-6,
author = {Jason Greene Boynton},
title = {Atomicity and the fixed divisor in certain pullback constructions},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {87-97},
zbl = {1261.13010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-6}
}
Jason Greene Boynton. Atomicity and the fixed divisor in certain pullback constructions. Colloquium Mathematicae, Tome 126 (2012) pp. 87-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-6/