# Answer to Question #24883 in Abstract Algebra for john.george.milnor

Question #24883

Let N1(R) be the sum of all nilpotent ideals in a ring R. Show that N1(R) is a nil subideal of Nil*R which contains all nilpotent one-sided ideals of R.

Expert's answer

Let

*N*=*N*1(*R*).Note that any nilpotent ideal is in Nil**R*, so*N**⊆*Nil**R*, and*N*is nil. If A is a nilpotent (say) left ideal,then A*R*is a nilpotent ideal, so A*⊆*A*R**⊆**N*.
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