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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
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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

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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