A remark on the commutativity of certain rings
HTML articles powered by AMS MathViewer
- by Ram Awtar PDF
- Proc. Amer. Math. Soc. 41 (1973), 370-372 Request permission
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.References
- Ram Niwas Gupta, Nilpotent matrices with invertible transpose, Proc. Amer. Math. Soc. 24 (1970), 572–575. MR 252408, DOI 10.1090/S0002-9939-1970-0252408-6
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
- Edward C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 95863, DOI 10.1090/S0002-9939-1957-0095863-0
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 370-372
- MSC: Primary 16A70
- DOI: https://doi.org/10.1090/S0002-9939-1973-0327842-9
- MathSciNet review: 0327842