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.
1
Expert's answer
2013-02-22T06:39:01-0500
Let N = N1(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 AR is a nilpotent ideal, so A ⊆AR ⊆ N.

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