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Non-commutative UFD's are often PID's

Published online by Cambridge University Press:  24 October 2008

M. P. Gilchrist  and
M. K. Smith
M. P. Gilchrist
Affiliation:
University of Leeds
M. K. Smith
Affiliation:
University of Texas
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Extract

The following concept of (not necessarily commutative) Noetherian unique factorization domain (UFD) was introduced recently by A. W. Chatters. Recall that an ideal P of a ring R is called completely prime if R/P is a domain. The element p∊R will be called a prime element if pR =Rp is a completely prime, height one prime of R. C(P) denotes the set of elements of R which are regular modulo P. Set C = ∩ C(P) where P ranges over the height one primes of R.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 3 , May 1984 , pp. 417 - 419
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

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