Non-commutative UFD's are often PID's
Published online by Cambridge University Press: 24 October 2008
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.
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- 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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