Chebotar, M.M.ChebotarLee, P-H.P-H.LeePuczylowski, E.R.E.R.Puczylowski2012-03-092018-06-282012-03-092018-06-282010http://ntur.lib.ntu.edu.tw//handle/246246/238975Let R be a simple ring with nontrivial zero-divisors. It is proved that every commutator in R is a sum of nilpotent elements if R contains nontrivial idempotents, but it is not so if R does not. An example is also given to show that not every commutator in a prime ring with nontrivial idempotents can be expressed as a sum of nilpotent elements.en-USjournal article10.1112/blms/bdp089http://ntur.lib.ntu.edu.tw/bitstream/246246/238975/-1/129.pdf