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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Smertnig, Daniel 2016. Multiplicative Ideal Theory and Factorization Theory.


    MacKenzie, Kenneth W. 1994. Polycyclic group rings and unique factorisation rings. Glasgow Mathematical Journal, Vol. 36, Issue. 02, p. 135.


    Chatters, A. W. Gilchrist, M. P. and Wilson, D. 1992. Unique factorisation rings. Proceedings of the Edinburgh Mathematical Society, Vol. 35, Issue. 02, p. 255.


    Gilchrist, Martin 1989. Non-commutative Noetherian Unique Factorization Domains often have stable range one. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 106, Issue. 02, p. 229.


    Whelan, E. A. 1988. An infinite construction in ring theory. Glasgow Mathematical Journal, Vol. 30, Issue. 03, p. 349.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 95, Issue 3
  • May 1984, pp. 417-419

Non-commutative UFD's are often PID's

  • M. P. Gilchrist (a1) and M. K. Smith (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004100061727
  • Published online: 24 October 2008
Abstract

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 pR 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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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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