ON NILPOTENT-DUO RINGS

A ring R is called right (resp., left) nilpotent-duo if N (R)a ⊆ aN (R) (resp., aN (R) ⊆ N (R)a) for every a ∈ R, where N (R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.