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Answer to Question #24890 in Abstract Algebra for Melvin Henriksen

Question #24890
Let I be a left ideal in a ring R such that, for some integer n, an = 0 for all a ∈ I. Show that I ⊆ Nil*R.
Expert's answer
Let J = Nil*R. If theimage I of I in R/J is nonzero, then there is a nonzeronilpotent ideal in R/J, which is impossible. Therefore, we must have I= 0, that is, I ⊆Nil*R.

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