Definition:Nilpotent Ring Element
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Definition
Let $R$ be a ring with zero $0_R$.
An element $x \in R$ is nilpotent if and only if:
- $\exists n \in \Z_{>0}: x^n = 0_R$
Also see
- Results about nilpotent ring elements can be found here.
Special cases
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $9$: Rings: Exercise $11$