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## Main Question or Discussion Point

let [tex] R[/tex] be a non-commutative ring and [tex] D(R)[/tex] denotes the set of zero-divisors of the ring . Suppose that [tex]z^{2} =0 [/tex] for any [tex]z \in D(R)[/tex] . prove that [tex]D(R)[/tex] is an ideal of [tex]R[/tex].