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

 

A remark on the commutativity of certain rings


Author: Ram Awtar
Journal: Proc. Amer. Math. Soc. 41 (1973), 370-372
MSC: Primary 16A70
MathSciNet review: 0327842
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Abstract: In a recent paper [1] Gupta proved that a division ring satisfying the polynomial identity $ x{y^2}x = y{x^2}y$ is commutative. In this note our goal is to prove the following: If $ R$ is a semiprime ring with $ x{y^2}x - y{x^2}y$ central in $ R$, for all $ x,y$ in $ R$, then $ R$ is commutative.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0327842-9
PII: S 0002-9939(1973)0327842-9
Keywords: Prime ring, semiprime ring, inner derivation, subdirect sum
Article copyright: © Copyright 1973 American Mathematical Society