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.

 

Integral domains with finitely generated groups of divisibility
HTML articles powered by AMS MathViewer

by D. D. Anderson PDF
Proc. Amer. Math. Soc. 112 (1991), 613-618 Request permission

Abstract:

Let $D$ be an integral domain with integral closure $\overline D$. We show that the group of divisibility $G(D)$ of $D$ is finitely generated if and only if $G(\overline D )$ is finitely generated and $\overline D /[D:\overline D ]$ is finite. We also show that $G(D)$ is finitely generated if and only if the monoid of finitely generated fractional ideals of $D$ (under multiplication) is finitely generated.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13A05, 13G05
  • Retrieve articles in all journals with MSC: 13A05, 13G05
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 613-618
  • MSC: Primary 13A05; Secondary 13G05
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1055765-X
  • MathSciNet review: 1055765