Length functions on integral domains
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- by David F. Anderson and Paula Pruis PDF
- Proc. Amer. Math. Soc. 113 (1991), 933-937 Request permission
Abstract:
Let $R$ be an integral domain and $x \in R$ which is a product of irreducible elements. Let $l(x)$ and $L(x)$ denote respectively the inf and sup of the lengths of factorizations of $x$ into a product of irreducible elements. We show that the two limits, $\bar l(x)$ and $\bar L(x)$, of $l({x^n})/n$ and $L({x^n})/n$, respectively, as $n$ goes to infinity always exist. Moreover, for any $0 \leq \alpha \leq 1 \leq \beta \leq \infty$, there is an integral domain $R$ and an irreducible $x \in R$ such that $\bar l(x) = \alpha$ and $\overline L (x) = \beta$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 933-937
- MSC: Primary 13G05; Secondary 13A05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057742-1
- MathSciNet review: 1057742