Overrings of Half-Factorial Domains
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 437-442
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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.
Anderson, David F.; Chapman, Scott T.; Smith, William W. Overrings of Half-Factorial Domains. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 437-442. doi: 10.4153/CMB-1994-063-2
@article{10_4153_CMB_1994_063_2,
author = {Anderson, David F. and Chapman, Scott T. and Smith, William W.},
title = {Overrings of {Half-Factorial} {Domains}},
journal = {Canadian mathematical bulletin},
pages = {437--442},
year = {1994},
volume = {37},
number = {4},
doi = {10.4153/CMB-1994-063-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-063-2/}
}
TY - JOUR AU - Anderson, David F. AU - Chapman, Scott T. AU - Smith, William W. TI - Overrings of Half-Factorial Domains JO - Canadian mathematical bulletin PY - 1994 SP - 437 EP - 442 VL - 37 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-063-2/ DO - 10.4153/CMB-1994-063-2 ID - 10_4153_CMB_1994_063_2 ER -
%0 Journal Article %A Anderson, David F. %A Chapman, Scott T. %A Smith, William W. %T Overrings of Half-Factorial Domains %J Canadian mathematical bulletin %D 1994 %P 437-442 %V 37 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-063-2/ %R 10.4153/CMB-1994-063-2 %F 10_4153_CMB_1994_063_2
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