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Length Functions on Integral Domains

David F. Anderson and Paula Pruis
Proceedings of the American Mathematical Society
Vol. 113, No. 4 (Dec., 1991), pp. 933-937
DOI: 10.2307/2048767
Stable URL: http://www.jstor.org/stable/2048767
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Length Functions on Integral Domains
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Abstract

Let R be an integral domain and x ∈ 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, l̄(x) and L̄(x), of l(xn)/n and L(xn)/n, respectively, as n goes to infinity always exist. Moreover, for any 0 ≤ α ≤ 1 ≤ β ≤ ∞, there is an integral domain R and an irreducible x ∈ R such that l̄(x) = α and L̄(x) = β.

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