Answer to Question #24895 in Abstract Algebra for Hym@n B@ss
Let R ⊆ S be rings. Show that R ∩ Nil*(S) ⊆ Nil*(R).
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).
No comments. Be first!