Journal article
Rational elasticity of factorizations in krull domains
Proceedings of the American Mathematical Society, Vol.117, pp.37-43
1993
DOI: 10.1090/S0002-9939-1993-1106176-1
Abstract
For an atomic domain R, we define the elasticity of R as p(R) = sup(m/n Ɩ x1 … xm, y1 … yn for xi, yj ∈ R irreducibles) and let lr(x) and LR(x) denote, respectively, the inf and sup of the lengths of factorizations of a nonzero nonunit x ∈ R into the product of irreducible elements. We answer affirmatively two rationality conjectures about factorizations. First, we show that p(R) is rational when R is a Krull domain with finite divisor class group. Secondly, we show that when R is a Krull domain, the two limits ln and LR(xn)/n, as n goes to infinity, are positive rational numbers. These answer, respectively, conjectures of D. D. Anderson and D. F. Anderson, and D. F. Anderson and P. Pruis. (The second question has also been solved by A. Geroldinger and F. Halter-Koch.). © 1993 American Mathematical Society.
Details
- Title: Subtitle
- Rational elasticity of factorizations in krull domains
- Creators
- D.D. AndersonD.F. AndersonS.T. ChapmanW.W. Smith
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.117, pp.37-43
- DOI
- 10.1090/S0002-9939-1993-1106176-1
- ISSN
- 0002-9939
- Language
- English
- Date published
- 1993
- Academic Unit
- Mathematics
- Record Identifier
- 9984230627002771
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