# Answer to Question #24895 in Abstract Algebra for Hym@n B@ss

Question #24895

Let R ⊆ S be rings. Show that R ∩ Nil*(S) ⊆ Nil*(R).

Expert's answer

Let

*r**∈**R ∩*Nil*(*S*). Consider any*m*-system*M*of the ring*R*such that*r**∈**M*. By definition,*M*is also an*m*-systemof*S*, so 0*∈**M*since*r**∈*Nil*(*S*). It follows that*r**∈*Nil*(*R*).Need a fast expert's response?

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