Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1322910
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A05, 13A15, 13E05, 13G05

Retrieve articles in all journals with MSC (1991): 13A05, 13A15, 13E05, 13G05


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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society