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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
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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.

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