Hostname: page-component-cb9f654ff-pvkqz Total loading time: 0 Render date: 2025-09-08T14:15:46.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Simple Properties of Simple Nil Rings

Published online by Cambridge University Press:  20 November 2018

W. A. McWorter
W. A. McWorter*
Affiliation:
University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An outstanding unsolved problem in the theory of rings is the existence or non-existence of a simple nil ring. Such a ring cannot be locally nilpotent as is well known [ 5 ]. Hence, if a simple nil ring were to exist, it would follow that there exists a finitely generated nil ring which is not nilpotent. This seemed an unlikely situation until the appearance of Golod's paper [ 1 ] where a finitely generated, non-nilpotent ring is constructed for any d ≥ 2 generators over any field.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 197 - 200
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Golod, E.S., On Nil Algebras and Finitely Approximabie p-Groups, (Russian), Izv. Akad. Nauk. SSSR Ser. Mat. vol. 28, (1964), 273-276.Google Scholar
2. Herstein, I.N. and Lance, Small, Nil Rings Satisfying Certain Chain Conditions, Canad. J. Math. vol. 16, (1964), 771-776.Google Scholar
3. Otto, Kegel, On Rings That Are Sums of two suorings, Journal of Algebra, vol 1 (1964), 103-109.Google Scholar
4. Jacob, Levitzki, On Nil Subrings, Israel J. Math. vol. 1, (1963), 215-216.Google Scholar
5. Szasz, F., Bemerkung liber Rechtesockel und Nilrings, Monatsh. Math. vol. 67, (1963), 359-362.Google Scholar