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$ t$-linked overrings of Noetherian weakly factorial domains

Authors: Mary B. Martin and M. Zafrullah
Journal: Proc. Amer. Math. Soc. 115 (1992), 601-604
MSC: Primary 13F15; Secondary 13B22, 13E05
MathSciNet review: 1081699
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Abstract: An integral domain $ D$ is a WFD if each nonzero nonunit of $ D$ is a product of primary elements of $ D$. We show that each $ t$-linked overring of a Noetherian WFD is again a WFD. This leads to the conclusion that the integral closure of a Noetherian WFD is a UFD.

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  • [1] D. D. Anderson and L. A. Mahaney, On primary factorizations, J. Pure Appl. Algebra 54 (1988), 141-154. MR 963540 (89h:13004)
  • [2] D. D. Anderson and M. Zafrullah, Weakly factorial domains and groups of divisibility, Proc. Amer. Math. Soc. 109 (1990), 907-913. MR 1021893 (90k:13015)
  • [3] D. Dobbs, E. Houston, T. Lucas, and M. Zafrullah, $ t$-linked overrings and Prüfer $ v$multiplication domains, Comm. Algebra 17 (1989), 2835-2852. MR 1025612 (90j:13016)
  • [4] R. W. Gilmer, Multiplicative ideal theory, Marcel Dekker, New York, 1972. MR 0427289 (55:323)
  • [5] J. Querré, Sur une propriete des anneaux de Krull, Bull. Sci. Math. (2) 95 (1971), 341-354. MR 0299596 (45:8644)
  • [6] N. Raillard, Sur les anneaux de Mori, thesis, Paris VI, 1976. MR 0379482 (52:387)
  • [7] M. Zafrullah, A general theory of almost factoriality, Manuscripta Math. 51 (1985), 29-62. MR 788672 (86m:13023)

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Article copyright: © Copyright 1992 American Mathematical Society

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