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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some commutativity results for rings with two-variable constraints


Author: H. E. Bell
Journal: Proc. Amer. Math. Soc. 53 (1975), 280-284
MSC: Primary 16A70
DOI: https://doi.org/10.1090/S0002-9939-1975-0382357-9
MathSciNet review: 0382357
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Abstract: It is proved that an associative ring $ R$ has nil commutator ideal if for each $ x,\;y\epsilon R$, there is a polynomial $ p(X)\epsilon X{\mathbf{Z}}[X]$ for which $ xy - yp(x)$ is central. Two restrictions on the $ p(X)$ which guarantee commutativity are established.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0382357-9
Article copyright: © Copyright 1975 American Mathematical Society