Geodesic
Atomicity and the fixed divisor in certain pullback constructions
Jason Greene Boynton1
1 Department of Mathematics North Dakota State University Fargo, ND 58108-6050, U.S.A.
Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 87-97.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $D$ be an integral domain with field of fractions $K.$ In this article, we use a certain pullback construction in the spirit of $\mathop {\rm Int}(E,D)$ 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.
DOI : 10.4064/cm129-1-6
Keywords: integral domain field fractions article certain pullback construction spirit mathop int furnishes many examples domains between which there elements admit finite factorization irreducible elements define notion fixed divisor pullback construction characterize its irreducible elements those nonzero nonunits admit finite factorization irreducibles route these characterizations construction yields domain infinite restricted elasticity

Jason Greene Boynton 1

1 Department of Mathematics North Dakota State University Fargo, ND 58108-6050, U.S.A. 
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Jason Greene Boynton. Atomicity and the fixed divisor in certain
 pullback constructions. Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 87-97. doi : 10.4064/cm129-1-6. http://geodesic.mathdoc.fr/articles/10.4064/cm129-1-6/

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