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Let <math>x\,</math> be a nilpotent element of the commutative ring <math>R\,</math>. Let <math>x^m=0\,</math> for minimal <math>m\isin \mathbb{Z}^+\,</math>. Prove that <math>rx\,</math> is nilpotent for all <math>r\isin R\,</math>.


<math>(rx)^m=r^mx^m=r^m\cdot 0=0\,</math>


[[Main Page]] : [[Abstract Algebra]] : [[Abstract Algebra#Rings| Rings]]

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