Length functions on integral domains

Authors:
David F. Anderson and Paula Pruis

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

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Abstract: Let be an integral domain and which is a product of irreducible elements. Let and denote respectively the inf and sup of the lengths of factorizations of into a product of irreducible elements. We show that the two limits, and , of and , respectively, as goes to infinity always exist. Moreover, for any , there is an integral domain and an irreducible such that and .

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1057742-1

Article copyright:
© Copyright 1991
American Mathematical Society