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Unique factorization in rings with right ACC1

Published online by Cambridge University Press:  18 May 2009

H. H. Brungs
H. H. Brungs
Affiliation:
Department of Mathematics, University of Alberta, Edmonton Alberta, Canada
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If R is an integral domain with maximum condition for principal right ideals—right ACC1—every nonzero non-unit in Rhas irreducible factors, but is not necessarily a product of such factors. Using additional basic factors—called infinite primes in [1]—results about unique factorization in principal right ideal domains have been obtained in [1], [2], and [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 167 - 171
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Beauregard, R. A., Infinite primes and unique factorization in a principal right ideal domain, Trans. Amer. Math. Soc. 141 (1969), 245–253.CrossRefGoogle Scholar
2.Brungs, H. H., Generalized discrete valuation rings, Canad. J. Math. 21 (1969), 1404–1408.CrossRefGoogle Scholar
3.Brungs, H. H., Ringe mit eindeutiger Faktorzerlegung, J. Reine Angew. Math. 236 (1969), 45–66.Google Scholar
4.Cohn, P. M., Free rings and their relations (Academic Press, 1971).Google Scholar
5.Jategaonkar, A., Left principal ideal rings, Lecture Notes in Mathematics 123 (Springer-Verlag, 1970).CrossRefGoogle Scholar