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Finite factorization domains

Author(s): D. D. Anderson; Bernadette Mullins
Journal: Proc. Amer. Math. Soc. 124 (1996), 389-396.
MSC (1991): Primary 13A05, 13A15, 13E05, 13G05
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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.

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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
Address at time of publication: Department of Mathematics, Youngstown State University, Youngstown, Ohio 44555
Email: bmullins@math.ysu.edu

DOI: 10.1090/S0002-9939-96-03284-4
PII: S 0002-9939(96)03284-4
Keywords: Finite factorization domain (FFD)
Received by editor(s): September 1, 1994
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1996, American Mathematical Society

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