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Some commutativity results for rings

Published online by Cambridge University Press:  17 April 2009

Abraham A. Klein ,
Itzhak Nada  and
Howard E. Bell
Abraham A. Klein
Affiliation:
Department of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel
Itzhak Nada
Affiliation:
Department of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel
Howard E. Bell
Affiliation:
Department of Mathematics, Brock University, St Catharines, Ontario, Canada L2S 3A1.
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Abstract

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It is proved that certain rings satisfying generalized-commutator constraints of the form [xm, yn, yn, …, yn] = 0 must have nil commutator ideal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 285 - 289
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Ананьин, А.З., Зябко, Е.М. [Anan'in, A.Z., Zyabko, E.M.], “Об одном вопросе Фейко” [On a question due to Faith], Algebra i Logika 13 (1974), 125–131.Google ScholarPubMed
[2]Herstein, I.N., “A commutativity theorem”, J. Algebra 38 (1976), 112–118.CrossRefGoogle Scholar
[3]Herstein, I.N., “On rings with a particular variable identity”, J. Algebra 62 (1980), 346–357.CrossRefGoogle Scholar
[4]Jacobson, Nathan, Structure of rings (Amer. Math. Soc. Colloquium Publications, 37. American Mathematical Society, Providence, Rhode Island, 1956. Revised edition, 1964).Google Scholar