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Proceedings of the American Mathematical Society

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

 
 

 

Rings satisfying monomial identities


Authors: Mohan S. Putcha and Adil Yaqub
Journal: Proc. Amer. Math. Soc. 32 (1972), 52-56
MSC: Primary 16.49
DOI: https://doi.org/10.1090/S0002-9939-1972-0289569-0
MathSciNet review: 0289569
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Abstract: The following theorem is proved: Suppose R is an associative ring and suppose that $ w({x_1}, \cdots ,{x_n})$ is a fixed word distinct from $ {x_1} \cdots {x_n}$. If, further, $ {x_1} \cdots {x_n} = w({x_1}, \cdots ,{x_n})$, for all $ {x_1}, \cdots ,{x_n}$ in R, then the commutator ideal of R is nilpotent. Moreover, it is shown that this theorem need not be true if the word w is not fixed.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289569-0
Article copyright: © Copyright 1972 American Mathematical Society

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