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Overrings of Half-Factorial Domains

Published online by Cambridge University Press:  20 November 2018

David F. Anderson ,
Scott T. Chapman  and
William W. Smith
David F. Anderson
Affiliation:
Department of Mathematics, The University of Tennessee Knoxville, Tennessee 37996 U.S.A.
Scott T. Chapman
Affiliation:
Department of Mathematics, Trinity University 715 Stadium Drive San Antonio, Texas 78212-7200 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

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An atomic integral domain D is a half-factorial domain (HFD) if for any irreducible elements α1,..., αn, β1,..., βm of D with α1... αn = β1 ...βm, then n = m. In [3], Anderson, Anderson, and Zafrullah explore factorization problems in overrings of HFDs and ask whether a localization of a HFD is again a HFD. We construct an example of a Dedekind domain which is a HFD, but with a localization which is not a HFD. We also give an example of a Dedekind domain where each localization is a HFD, but with an overring which is not a HFD.

Keywords

Primary: 13F05secondary: 13F1513G0513A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 437 - 442
Copyright
Copyright © Canadian Mathematical Society 1994

References

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