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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Words periodic over the center of a division ring


Authors: Leonid Makar-Limanov and Peter Malcolmson
Journal: Proc. Amer. Math. Soc. 93 (1985), 590-592
MSC: Primary 16A39; Secondary 16A70
MathSciNet review: 776184
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Abstract: In generalization of a result of Herstein, the authors prove that, in a division ring with uncountable center, if any given nontrivial group word takes only values periodic over the center, then the division ring is commutative. Techniques include use of the result that a noncommutative division ring finite-dimensional over its center includes a nonabelian free group in its multiplicative group.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776184-4
PII: S 0002-9939(1985)0776184-4
Article copyright: © Copyright 1985 American Mathematical Society