Finite factorization domains
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- by D. D. Anderson and Bernadette Mullins PDF
- Proc. Amer. Math. Soc. 124 (1996), 389-396 Request permission
Abstract:
An integral domain $R$ is a finite factorization domain if each nonzero element of $R$ has only finitely many divisors, up to associates. We show that a Noetherian domain $R$ is an FFD $\Leftrightarrow$ for each overring $R’$ of $R$ that is a finitely generated $R$-module, $U(R’)/U(R)$ is finite. For $R$ local this is also equivalent to each $R/[R:R’]$ being finite. We show that a one-dimensional local domain $(R,M)$ is an FFD $\Leftrightarrow$ either $R/M$ is finite or $R$ is a DVR.References
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Additional Information
- D. D. Anderson
- Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
- Email: dan-anderson@uiowa.edu
- Bernadette Mullins
- Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
- Email: bmullins@math.ysu.edu
- Received by editor(s): September 1, 1994
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 389-396
- MSC (1991): Primary 13A05, 13A15, 13E05, 13G05
- DOI: https://doi.org/10.1090/S0002-9939-96-03284-4
- MathSciNet review: 1322910