Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T01:02:09.812Z Has data issue: false hasContentIssue false
  • English
  • Français

On automorphisms of unique factorization domains

Published online by Cambridge University Press:  24 October 2008

M. L. Brown
M. L. Brown
Affiliation:
Department of Mathematics, University of Exeter, Exeter, EX4 4QE
Get access Rights & Permissions [Opens in a new window]

Extract

Chatters has asked whether a unique factorization domain (UFD) R, equipped with an automorphism σ transitive on the height 1 prime ideals of R, is necessarily Dedekind. If R contains an uncountable field, then Chatters observed that the answer is affirm ative. In this note was show:

Theorem. Let R be a local UFD equipped with an automorphism σ which is transitive on the height 1 prime ideals of R. Suppose that σ induces an automorphism of finite order on the residue field κ of R (for example, if κ is a global or finite field), Then R is Dedekind.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 427 - 428
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCE

[1]Brown, M. L.. A note on euclidean rings of affine curves. J. London Math. Soc. (2) 29 (1984), 229–236.CrossRefGoogle Scholar