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-systemM 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).

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