Abstract
AbstractIt is shown that ifN(R) is a Lie ideal ofR(respectively Jordan ideal andRis 2-torsion-free), thenN(R) is an ideal. Also, it is presented a characterization of Noetherian NR rings with central idempotents (respectively with the commutative set of nilpotent elements, the Abelian unit group, the commutative commutator set).
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