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On transposes of nilpotent matrices over arbitrary rings

Published online by Cambridge University Press:  09 April 2009

Thomas P. Kezlan
Thomas P. Kezlan
Affiliation:
Department of Mathematics, University of Missouri — Kansas City, Kansas City, Missouri 64110, U.S.A.
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Abstract

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It is shown that if every nilpotent 2 × 2 matrix over a ring has nilpotent transpose, then the commutator ideal must be contained in the Jacobson radical, thus generalizing a result of R. S. Gupta, who considered the division ring case. Moreover, if the nilpotent elements form an ideal or if the ring satisfies a polynomial identity, then the above property of the transpose implies that in fact the commutator ideal must be nil.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 366 - 370
Copyright
Copyright © Australian Mathematical Society 1977

References

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