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Nil Rings Satisfying Certain Chain Conditions: An Addendum

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein  and
Lance Small
I. N. Herstein
Affiliation:
The University of Chicago
Lance Small
Affiliation:
The University of Chicago
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We prove here a result closely related both in spirit and technique to those obtained in our paper (1). We also take this opportunity to present a counter example, due to E. Sąsiada, to the conjecture we made there. Finally, we extend a result of Wedderburn (3) from algebras over fields to algebras over commutative rings; the result follows easily from the paper by Posner (2) although it does not appear there explicitly.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 300 - 302
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Herstein, I. N. and Small, Lance, Nil rings satisfying certain chain conditions, Can. J. Math., 16,(1964), 771–776.Google Scholar
2. Posner, E., Prime rings satisfying polynomial identities, Proc. Amer. Math. Soc., 11 (1962), 180–184.Google Scholar
3. Wedderburn, J. H. M.. Note on algebras, Ann. of Math., 38 (1937), 854–856.Google Scholar