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Atomicity and the fixed divisor in certain pullback constructions

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Boynton J.

Colloquium Mathematicum

2012

tom 129

nr 1

87-97

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.

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1 Colloquium Mathematicum

1 Boynton J.

1 2012

Wyniki wyszukiwania

Atomicity and the fixed divisor in certain pullback constructions