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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