Hostname: page-component-cc8bf7c57-7lvjp Total loading time: 0 Render date: 2024-12-11T01:18:24.512Z Has data issue: false hasContentIssue false

Some commutativity results for rings

Published online by Cambridge University Press:  17 April 2009

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.
Rights & Permissions [Opens in a new window]

Abstract

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.

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
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), 125131.Google ScholarPubMed
[2]Herstein, I.N., “A commutativity theorem”, J. Algebra 38 (1976), 112118.CrossRefGoogle Scholar
[3]Herstein, I.N., “On rings with a particular variable identity”, J. Algebra 62 (1980), 346357.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