Skip to main content Accessibility help
×
Home

The fundamental prime ideals of a noetherian prime PI ring

  • T. H. Lenagan (a1) and Edward S. Letzter (a2)

Abstract

Let R be a noetherian prime PI ring and let P be a prime ideal of R. There is a set of prime ideals, the fundamental prime ideals, associated with the injective hull of R/P and denoted by Fund(P). The set Fund(P) is finite, by a result of Miiller. In this paper we give a natural description of Fund(P) in terms of the trace ring of R which strengthens Miiller's result by establishing a uniform bound for the size of Fund(P) for all primes P in the ring.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The fundamental prime ideals of a noetherian prime PI ring
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The fundamental prime ideals of a noetherian prime PI ring
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The fundamental prime ideals of a noetherian prime PI ring
      Available formats
      ×

Copyright

References

Hide All
1.Braun, A., An additivity principle for PI rings, J. Algebra 96 (1985), 433441.
2.Braun, A. and Small, L. W., Localization in prime noetherian PI rings, Math. Z. 193 (1986), 323330.
3.Braun, A. and Warfield, R. B. JR., Symmetry and localization in noetherian prime PI rings, J. Algebra, to appear.
4.Brown, K. A. and Warfield, R. B. JR., The influence of ideal structure on representation theory, J. Algebra 116 (1988), 294315.
5.Jategaonkar, A. V., Localization in Noetherian Rings (London Math. Soc. Lecture Note, Vol. 98, Cambridge Univ. Press, Cambridge, 1986).
6.Krause, G. R., On fully left bounded left noetherian rings, J. Algebra 23 (1972), 8899.
7.Letzter, E. S., Prime ideals in finite extensions of noetherian rings, J. Algebra, to appear.
8.Mcconnell, J. C. and Robson, J. C.. Noncommutative Noetherian Rings (Wiley, New York, 1988)
9.Moller, B. J., Localization in fully bounded noetherian rings, Pacific J. Math. 67 (1976), 233245.
10.Muller, B. J., Two-sided localization in noetherian PI rings, J. Algebra 63 (1980), 359373.
11.Robson, J. C., Prime ideals in ntermediate extensions, Proc. London Math. Soc. (3) 44 (1982), 372384.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

The fundamental prime ideals of a noetherian prime PI ring

  • T. H. Lenagan (a1) and Edward S. Letzter (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.