Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Finite factorization domains
HTML articles powered by AMS MathViewer

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
Similar Articles
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