Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-18T19:05:00.455Z Has data issue: false hasContentIssue false
  • English
  • Français

Unique factorisation of normal elements in polynomial rings

Published online by Cambridge University Press:  14 November 2011

D.A. Jordan
D.A. Jordan
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

We consider the class of Noetherian UFN-rings, that is, Noetherian prime rings such that every non-zero ideal contains a non-zero normal element and such that the monoid of non-zero normal elements is a unique factorisation monoid. We ask whether this class of rings, a generalisation of the commutative Noetherian unique factorisation domains (UFD), is closed under polynomial extensions. The general question is apparently difficult and remains open. However, we give positive answers in special cases, in particular, for algebras over an infinite field and for domains.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 241 - 247
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Chatters, A. W.. Non-commutative unique factorisation domains. Math. Proc. Cambridge Philos. Soc. 95 (1984), 49–54.CrossRefGoogle Scholar
2Chatters, A. W. and Jordan, D. A.. Non-commutative unique factorisation rings. J. London Math. Soc. (2) 33 (1986), 22–32.CrossRefGoogle Scholar
3Cohn, P. M.. Free rings and their relations. London Math. Soc. Monograph 19, 2nd edn (London: Academic Press, 1985).Google Scholar
4Jordan, D. A.. Unique factorisation of normal elements in non-commutative rings. Glasgow Math. J. (to appear).Google Scholar
5McConnell, J. C. and Robson, J. C.. Non-commutative Noetherian rings (Chichester: Wiley, 1987).Google Scholar
6Sharpe, D. W.. Rings and factorization (Cambridge: Cambridge University Press, 1987).CrossRefGoogle Scholar