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Hereditary Local Rings

Published online by Cambridge University Press:  22 January 2016

P. M. Cohn
P. M. Cohn*
Affiliation:
Queen Mary College, University of London
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Many questions about free ideal rings ( = firs, cf. [5] and §2 below) which at present seem difficult become much easier when one restricts attention to local rings. One is then dealing with hereditary local rings, and any such ring is in fact a fir (§2). Our object thus is to describe hereditary local rings. The results on firs in [5] show that such a ring must be a unique factorization domain; in §3 we prove that it must also be rigid (cf. the definition in [3] and §3 below). More precisely, for a semifir R with prime factorization rigidity is necessary and sufficient for R to be a local ring.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 223 - 230
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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