Finite factorization domains

Authors:
D. D. Anderson and Bernadette Mullins

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

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Abstract | References | Similar Articles | Additional Information

Abstract: An integral domain is a *finite factorization domain* if each nonzero element of has only finitely many divisors, up to associates. We show that a Noetherian domain is an FFD for each overring of that is a finitely generated -module, is finite. For local this is also equivalent to each being finite. We show that a one-dimensional local domain is an FFD either is finite or 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

Email:
bmullins@math.ysu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03284-4

Keywords:
Finite factorization domain (FFD)

Received by editor(s):
September 1, 1994

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society