Atomicity and the fixed divisor in certain pullback constructions

• Autorzy: Jason Greene Boynton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13G05: Integral domains
• 13F15: Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
• 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
• 13A05: Divisibility; factorizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 87-97

Daty

wydano

2012

Twórcy

autor

Jason Greene Boynton

• Department of Mathematics, North Dakota State University, Fargo, ND 58108-6050, U.S.A.

Identyfikatory

DOI

10.4064/cm129-1-6