Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:30:53.762Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of unique factorization rings

Published online by Cambridge University Press:  24 October 2008

C. R. Fletcher
C. R. Fletcher
Affiliation:
University College of Wales, Aberystwyth
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. In (1) we proved that the direct sum of a finite number of unique factorization rings is a unique factorization ring (UFR), and in particular that the direct sum of a finite number of unique factorization domains (UFD's) is a UFR. The converse, however, does not hold i.e. not every UFR can be expressed as a direct sum of UFD's. Here we investigate the structure of UFR's and show that every UFR is a finite direct sum of UFD's and of special UFR's. There is thus a relationship with the structure theorem for principal ideal rings ((2), p. 245).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 535 - 540
Copyright
Copyright © Cambridge Philosophical Society 1970

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

REFERENCES

(1)Fletcher, C. R.Unique Factorization Rings. Proc. Cambridge Philos. Soc. 65 (1969), 579–583.CrossRefGoogle Scholar
(2)Zariski, O. and Samuel, P.Commutative Algebra, vol. 1 (Princeton, 1958).Google Scholar