Atomicity and the fixed divisor in certain pullback constructions

Jason Greene Boynton. "Atomicity and the fixed divisor in certain pullback constructions." Colloquium Mathematicae 129.1 (2012): 87-97. <http://eudml.org/doc/283713>.

@article{JasonGreeneBoynton2012,
abstract = {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.},
author = {Jason Greene Boynton},
journal = {Colloquium Mathematicae},
keywords = {atomic domains; pullbacks; integer-valued polynomials},
language = {eng},
number = {1},
pages = {87-97},
title = {Atomicity and the fixed divisor in certain pullback constructions},
url = {http://eudml.org/doc/283713},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Jason Greene Boynton
TI - Atomicity and the fixed divisor in certain pullback constructions
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 87
EP - 97
AB - 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.
LA - eng
KW - atomic domains; pullbacks; integer-valued polynomials
UR - http://eudml.org/doc/283713
ER -