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nilpotent ideal

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Definition

For nn a positive integer and II a (left) ideal of a ring RR, let I nI^n denote the ideal of RR consisting of all finite sums of nn-tuple products i 1i ni_1\cdots i_n of elements in II.

Definition

A (left) ideal II of a ring RR is nilpotent if there exists a positive natural number nn such that I nI^n is the zero ideal of RR.

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