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On the k-HFD property in Dedekind domains with small class group

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  26 February 2010

Scott T. Chapman  and
William W. Smith
Scott T. Chapman
Affiliation:
Department of Mathematics, Trinity University, 715 Stadium Drive, San Antonio, Texas 78212, U.S.A.
William W. Smith
Affiliation:
Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, U.S.A.
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Abstract

Let D be an atomic integral domain (i.e., a domain in which each nonzero nonunit of D can be written as a product of irreducible elements) and k any positive integer. D is known as a half factorial domain (HFD) if for any irreducible elements α1, …, αn, β1, …, βm of D the equality α1… αn = β1… βm implies that n = m. In [5] the present authors define D to be a k-half factorial domain (k-HFD) if the equality above along with the fact that n or m ≤ k implies that n = m. In this paper we consider the k-HFD property in Dedekind domains with small class group and prove the following Theorem: if D is a Dedekind domain with class group of order less than 16 then D is k-HFD for some integer k > 1, if, and only if, D is HFD.

MSC classification

Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 330 - 340
Copyright
Copyright © University College London 1992

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