AAR11

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Let x\, be a nilpotent element of the commutative ring R\,. Let x^m=0\, for minimal m\isin \mathbb{Z}^+\,. Prove that x\, is either zero or a zero divisor.

x^m=x(x^{m-1})=0\, so x=0\, or x\, is a zero divisor of the nozero element x^{m-1}\,.


Main Page : Abstract Algebra : Rings

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