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Abstract
Let be a non-commutative ring with center
and let
be the set of all nilpotents of
. The following result is proved: If for every
, there exists an integer
, depending on
, such that
, then
is one of five types whose structures can be determined abstractly.
ACKNOWLEDGMENT
The authors would like to thank the referee and Prof. M. Ferrero for their valuable comments and suggestions.
The research of the first author was done during his stay at the University of California, Santa Barbara, while visiting the Department of Mathematics in 1997.