AAR12

From Example Problems
Jump to: navigation, search

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


(rx)^{m}=r^{m}x^{m}=r^{m}\cdot 0=0\,


Main Page : Abstract Algebra : Rings