On prime rings with commuting nilpotent elements

Chebotar, M.; Lee, P.-H.; Puczyłowski, E.

doi:10.1090/S0002-9939-09-09894-3

On prime rings with commuting nilpotent elements
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by M. Chebotar, P.-H. Lee and E. R. Puczyłowski PDF

Proc. Amer. Math. Soc. 137 (2009), 2899-2903 Request permission

Abstract:

Let $R$ be a prime ring in which the nilpotent elements commute. If $R$ has finite right uniform dimension or its maximal right quotient ring is Dedekind finite, then $R$ contains no nonzero nilpotent elements.

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